Maths-
General
Easy
Question
Consider the cubic equation whose roots are x1, x2, and x3
The value of equals
- 1
- 2
- 2 cos
![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
![sin space theta left parenthesis sin space theta plus cos space theta right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJAAAAAQCAYAAAD59vZgAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAolJREFUeNrtWj1LA0EQPVKkCoKFBBERLEQkhICIhGAhiIUECQELCwsRRETsrWzFvyBiJTYSrEQQEREJgohICDYWFlbpLEREiLP4Iue495G9PW9P8uAhu3eebz52dvZOy4oHVolbVgdRYwuxiBWyxGondsbgCjFpG80QxBSIFeIz8YI47iA4FxOt/wFedo4SL01IoHEITWDcQ3xk9+SQQHHQ+h/g185LJFKkuCP2sbkTVh63iWsGONaP1r+uiFHauc570kHiOfEVxjZ9OKE1nkOWvqHk9fsQOkXck8wfEGeY+Al2j6ladSVQAdqExifiArteJNaJ7/g5K3mGHx8FsTNPPLNP3DgI8QrKHKrEAOYWYbwXdohlybwon9O28Qsxye4xVauOBBJbdoNYwjYyRNxnW4xYABmMMxjnFXwUxM4kYvMNkandCkGZZHMJrAwv1G0rgzNtu+9D8rumatWRQIfYHtyuFyUV6UjBR0Ht/OG7EprV+TaDouKsBM9el3lZApmqlT/XizKIZ3a5PFdWkZMSLX58FNTOX4svhTJWR+kMKyhpvn8CY1hhXg4zVauOCtRUvP6u4KMgdibdFtAG8TbEoLSOihyb6EvsOEVTGQetOhKooakC+fFREDvzDgnn2hvoCkoKx0U7umEkd47XMd4krToSaMdHDzQr2a4qCj4KYucaYiPFEo6AYQVFoGZz1LD19ami6HAqcXuRaJJWHQk0iKN7GYEX72R22ZYiTl0jGGcxLij4KIidv14ktho70bQeE3tDDkoWGS9Wxr3HkbPKXmSZrFUHxKK5hn13kr8ngvoAPTVUIKcm3s1HqnYqf8qICp2PqWZB+WNqlFixOv/OYQJE37Nsn/gEs98fLepbuxQAAADedEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnNpbjwvbWk+PG1vPiYjeEEwOzwvbW8+PG1pPiYjeDNCODs8L21pPjxtbz4oPC9tbz48bWk+c2luPC9taT48bW8+JiN4QTA7PC9tbz48bWk+JiN4M0I4OzwvbWk+PG1vPis8L21vPjxtaT5jb3M8L21pPjxtbz4mI3hBMDs8L21vPjxtaT4mI3gzQjg7PC9taT48bW8+KTwvbW8+PC9tYXRoPo6eJw4AAAAASUVORK5CYII=)
Hint:
In this question, we have given a cubic equation. which is
.
We have given roots is
. We have to find the
. For that use the do
and find the product of root and sum of root then substitute them into it.
The correct answer is: 2
Here we have to find the
.
We know that
![left parenthesis x 1 plus x 2 plus x 3 right parenthesis squared equals x 1 squared plus x 2 squared plus x 3 squared plus 2 left parenthesis x 1 x 2 plus x 2 x 3 plus x 3 x 1 right parenthesis](data:image/png;base64,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)
We have cubic equation that is ,
In this equation,
The sum of root =
![left parenthesis space x 1 space plus space x 2 space plus space x 3 space right parenthesis space equals space 1 plus cos theta plus sin theta space minus negative negative negative negative left parenthesis 1 right parenthesis](data:image/png;base64,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)
And product of roots = ![c over a](data:image/png;base64,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)
![x 1 x 2 space plus space x 2 x 3 space plus space x 3 x 1 space equals space cos theta space sin theta space plus space cos theta space plus space sin theta space minus negative negative negative negative negative left parenthesis 2 right parenthesis](data:image/png;base64,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)
we have,
![left parenthesis x 1 plus x 2 plus x 3 right parenthesis squared equals x 1 squared plus x 2 squared plus x 3 squared plus 2 left parenthesis x 1 x 2 plus x 2 x 3 plus x 3 x 1 right parenthesis](data:image/png;base64,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)
![equals greater than left parenthesis 1 plus c o s theta plus s i n theta right parenthesis squared equals x 1 squared plus x 2 squared plus x 3 squared plus 2 left parenthesis c o s theta s i n theta plus c o s theta plus s i n theta right parenthesis](data:image/png;base64,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)
![equals greater than 1 plus c o s squared theta plus s i n squared theta plus 2 c o s theta plus 2 c o s theta. s i n theta plus 2 s i n theta equals x 1 squared plus x 2 squared plus x 3 squared plus 2 c o s theta s i n theta plus 2 c o s theta plus 2 s i n theta](data:image/png;base64,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)
![equals greater than x 1 squared plus x 2 squared plus x 3 squared equals 1 plus left parenthesis c o s squared theta plus s i n squared theta right parenthesis plus left parenthesis 2 c o s theta plus 2 c o s theta. s i n theta plus 2 s i n theta right parenthesis – left parenthesis 2 c o s theta s i n theta plus 2 c o s theta plus 2 s i n theta right parenthesis](data:image/png;base64,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)
![equals greater than x 1 squared plus x 2 squared plus x 3 squared equals 1 plus 1 plus 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOsAAAARCAYAAAA8A1uqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAt1JREFUeNrtWj1IHEEUHkREgggiIpIiICJiEWzlEBFEJIgEweJIISJYpAq2YpUmVZAQAhIkhUUgSAhBRJCwiFgIEsRKbKxtLCzCIcL5HvcWl+N2b2Zudn4274MPbmdvdz5m53vz5u0KUWxUiffAE+AQ62bdDL/RBnwL/Mu6WTcjDFRYN+tm+I9J4BHrZt0MNxgGbgDPm/xvgPZQg471loC7wDva16HuNwHongLuA//RankF3AT2OtQt++xD6qsb+AV4StyitkJgB7gqakWNrIHeownkGrjSlIFddDxKk7rsue4IuADsSLSNAQ8c6pZ59qH19Qc4nzieo7bcJ2XJ4mSqZkT4fc3oVLWk/QXwIkDdgjIEU7pNP/s8xijPvhaBnxq0b6YEc2MYp4igatoV4IcG7e/pnOqA4MQZsfBgdHXHqASoG1PcS4O6/3ez4vZoJmULspt182bUMe245DVY7u9PHC8DP2sOSCvaVR+Mju54jE4C0t1P/8F966sWdJuaZ0Ux623dNiMGtt3YjH6xaSMJ084CP9LvacmcPY/UT/WeOro7qZBQCkB3vZHeeVK3KIpZHzLO3bsY2DVJ8YeiVvrH6luvJbOaiPQqunuAv1JSH991v6YgMxmIWW2u4rp9PShsk3JJg5MrayS5sgqK2hhNXjosqujcU1b3IBl1KDDdSXSRYV0GmSKtrDcpaXCnrTQ4Numxwp41fheJqVk5ILPK6sYCzFfgM0/SQp3xbhrxOQ3WKjDNNmifySowmTbphMJ1uOL8pomMkfvMYhrcyj1ldWNx5gew3ZPJqzveglbhKzarsWsWKIjX45vI+dWNqkkRfaJW+k9OFnwpvOO5WVV074n8X23koRur+YsUZPAjfXydcA1cYrMavSaiLUk7pcTrwsNPNlHYT+DzBue+p6QHwtB+2qZuk3UAm7onKNBUiBEZ27VJbY2hrb6weLdNY4yfdm6Jp6/dGAxGKHgEt1NTMtSdBuAAAAEndEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjxtbz4mZ3Q7PC9tbz48bWk+eDwvbWk+PG1zdXA+PG1uPjE8L21uPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT54PC9taT48bXN1cD48bW4+MjwvbW4+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1pPng8L21pPjxtc3VwPjxtbj4zPC9tbj48bW4+MjwvbW4+PC9tc3VwPjxtbz49PC9tbz48bW4+MTwvbW4+PG1vPis8L21vPjxtbj4xPC9tbj48bW8+KzwvbW8+PG1uPjA8L21uPjwvbWF0aD6AX1GrAAAAAElFTkSuQmCC)
![equals greater than x 1 squared plus x 2 squared plus x 3 squared equals 2](data:image/png;base64,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)
Therefore, the value of ![x 1 squared plus x 2 squared plus x 3 squared i s 2.](data:image/png;base64,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)
The correct answer is 2.
In this question, we have to given the cubic equation and its root x1,x2,x3 and we have to find the.Use,
and sum of roots is
and product of roots is b/a.
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The ratio of the gases obtained on dehydration ofHCOOH and ![H subscript 2 C subscript 2 O subscript 4 space b y space c o n c. H subscript 2 S O subscript 4](data:image/png;base64,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)
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