Maths-
General
Easy
Question
If
then K=
- -1
- -2
- -3
- -4
Hint:
- Take LCM on RHS and simplify
- Then take a value of x which satisfies the requirement.
The correct answer is: -4
Given :
![fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction](data:image/png;base64,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)
Taking LCM on RHS and factorizing on LHS
![rightwards double arrow fraction numerator x squared minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction equals fraction numerator A left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis space plus space B left parenthesis x minus 1 right parenthesis left parenthesis x minus 3 right parenthesis space plus space K left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction
rightwards double arrow x squared minus 10 x plus 13 space equals space A left parenthesis x squared space minus 5 x space plus 6 right parenthesis plus space B left parenthesis x squared minus 4 x space plus 3 right parenthesis space plus space K left parenthesis x squared space minus 3 x space plus 2 right parenthesis
rightwards double arrow x squared minus 10 x plus 13 space equals space A left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis space plus space B left parenthesis x minus 1 right parenthesis left parenthesis x minus 3 right parenthesis space plus space K left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis
P u t space x equals space 3
rightwards double arrow 9 minus 30 plus 13 space equals space 0 plus 0 right parenthesis space plus space 2 K
rightwards double arrow 2 K space equals space minus 8
rightwards double arrow space K space equals space minus 4](data:image/png;base64,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Related Questions to study
Maths-
If the remainders of the polynomial
when divided by
and
are 7,3 then the remainder of
when devided by
is
If the remainders of the polynomial
when divided by
and
are 7,3 then the remainder of
when devided by
is
Maths-General
Maths-
If
then ![fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals](data:image/png;base64,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)
If
then ![fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAAAnCAYAAADpYmEPAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA4ZJREFUeNrtnF+EVFEcx6+RkaxhZSUrkSQ9ZFhJRhL7kLUyeutxLEnWWoke1kgSax/2YfTSU1ayZM1DViJZa619SdY+JNFTRtaSJMkatt/Rd+x1nHPvmTv3z87t++HLzJ07M+d87++c8/uduzueR86I6qJNWkHi4LnolmiPVpA4YUARBhRhQBEGFCEMKMKAIgwoQhhQhAFF+iqQdBFCCCGEEBJnfsl8kxzcaKTyKUK45BFCCCEk8xxhV7QuOk1LkuWOaDYH/ZhFX2wU8PqHHPsQ5kHinBdt5GhwrKNPQfzJuQ8uHiT65eU+Meo3ZpkgRkRrAa9fEa32uQ9h3oR5kBhlGNkPqLxny/HcNZiqcxz9PdXHPrh6Y/MgUeZEkxkny65URYuO504ZciH1r+jLCKqD5EMcm4Ymb6ayyAffiC5bkteHom1URur3AE5q50xYGvwIr8Vt5gPRDNr1DXnQiiVALoneaTPTa1GpSx8UAwi4FrxoigYz8qDTnoboBzxYEj0R3Q/xIBV+ioqG48to9CCC6yVGgY6qlo75ntfQuSRGp2rDFxjXade8ZdYqom8dVDCdjeDDAPr4GMGozrknGs/IgwIGUQ2PSxhoe4bro3uQCm3DsZu4eH4WRGOGc6/hoipGI4yIbsz8LDqnHSsFmLarfU/Qval2QAneCGlXmh7UDTNRx5vhEA8yC6gVTJd+Vg1LXoe3qJzUsnjUwbwoNyELqGJ0DjsGVBQf1Hfu+Ja3INLwQPEVs6aLN5kElGmq10tz9fhXwGdMo+FR9j1cR+dFBHpYrhR1ujf5cKGL0jsND8qW7Q6bN5kseWpkVbRjO9rzimffWa4gKZzHUpmUmeqznxmO38Uy4Bpo3fgwhgQ8jLQ8uOH9+40rV28yScpN5XILS4l/3V4yvFft5bwSHcE0/N5huo9qZgOJqD4CtyxV3iT61osPag/nU8j70vSgashtPW//h9R69SAWTBt6quR9iqVO5U0vUCX5GcIxv3njlhEUh5lNJJ6jeD6MYzXL+d1u6tk2NjdR4R1CATDtm8nS9kAF7Udvfzd/BNV4y1IwZbKxqdgwrP0zGA11zFbbvrK0iItpqioWUfXEjfr+6wiqNi501XJu1NsOJh9OIG9pYzacyNADD9sTTew/qfZeFX3XVpRePIgFl5uiQ17/EPXGKG8Ox8htLx9/vjJnySf+Jx969cCJv5RUi5Zoci9qAAAA/nRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MTwvbW4+PG1yb3c+PG1vPig8L21vPjxtaT5hPC9taT48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5iPC9taT48bXN1cD48bW8+KTwvbW8+PG1uPjI8L21uPjwvbXN1cD48bW8+KDwvbW8+PG1pPmM8L21pPjxtaT54PC9taT48bW8+KzwvbW8+PG1pPmQ8L21pPjxtbz4pPC9tbz48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PC9tYXRoPq9hdg0AAAAASUVORK5CYII=)
Maths-General
Maths-
The partial fractions of
are
The partial fractions of
are
Maths-General
Maths-
The partial fractions of
are
The partial fractions of
are
Maths-General
Maths-
then ![A plus B minus C plus D equals](data:image/png;base64,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)
then ![A plus B minus C plus D equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHMAAAANCAYAAACaa1FXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAhhJREFUeNrtmE9ERFEUxp8xktGmRTJGIsms0iZpkTYjI0mGZCRJtEiLFpFWs0ibtBhJJGPMYsRIi6RNWrVok6RFiyFp2WYkycgwfZfvcY0373kz97xVH7/NfX+u757zzj33WZa7Nq1gVAU18A5ewSWICs43APbBE/jhvLugW9BfXeMblEB/QOtrLYBfEBaeZ5CLqkstbF5ovi1wBSZAiGN9TNx8AP5CTNQNJlFKOpAqQ5/BDZjz+Wzd5/3q/cWGsZTDmAltg9M232HCn6158KUllYhOQBosgyNhsxkusq4CSBr2NMQSHg44mBlWg2ZSJXdUKpDjLENKvVwASbMlZq/KzhGQE9qrDwy9txV/sy7Xb0GiyTxeuEpl7QP3EFuPIC5ottzQGCSFkvSF+1fQwSx7NHNvoEfCsFNJ2APrHuZazaAQA6jUwQy9Z0k0OVeIHWWrwTPhz0kR8CERyDi/wkZN8qggkbljLDO6FnlsMKkONhpWwF+mkz9dyy4NWVtl9s7lIT9HFD9m09wjdS0Z6DibNRqRgIPp5E+XOjEMmza6BrIu18/AtIDZQ7DSMJbjIphWzqOrtALyZyvrseYtKcoM6XK5Z9XHxH7MXmgNTw/PXU8si6al/rZUwI72p6cTzDDQCWF/drmfAtfgWGKvLNGQm2LsykyropXyKitATPhvU4H7p5rzE5z7qDrt+Kux2Sny+PevfzXXH6iCrW2uPfZEAAAAj3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5BPC9taT48bW8+KzwvbW8+PG1pPkI8L21pPjxtbz4tPC9tbz48bWk+QzwvbWk+PG1vPis8L21vPjxtaT5EPC9taT48bW8+PTwvbW8+PC9tYXRoPhs/t+IAAAAASUVORK5CYII=)
Maths-General
Maths-
The partial fractions of
are
The partial fractions of
are
Maths-General
Maths-
The partial fractions of
are
The partial fractions of
are
Maths-General
Maths-
If
then ![P left parenthesis x right parenthesis equals](data:image/png;base64,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)
If
then ![P left parenthesis x right parenthesis equals](data:image/png;base64,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)
Maths-General
Maths-
Let a,b,c such that
then ,
?
Let a,b,c such that
then ,
?
Maths-General
Maths-
If
then B=
If
then B=
Maths-General
Maths-
If the remainders of the polynomial f(x) when divided by
are 2,5 then the remainder of
when divided by
is
If the remainders of the polynomial f(x) when divided by
are 2,5 then the remainder of
when divided by
is
Maths-General
Maths-
Assertion :
can never become positive.
Reason : f(x) = sgn x is always a positive function.
Assertion :
can never become positive.
Reason : f(x) = sgn x is always a positive function.
Maths-General
Maths-
=
=
Maths-General
maths-
Evaluate
dx
Evaluate
dx
maths-General
maths-
If
. The integral of
with respect to
is -
If
. The integral of
with respect to
is -
maths-General