Mathematics
Grade10
Easy
Question
How many solutions are there for the equation 3
using the discriminant?
- 0
- 1
- 2
- Either 1 or 2
Hint:
Any equation of the form p (x) = 0, where p (x) is a polynomial of degree 2, is a quadratic equation
The correct answer is: 0
Step 1 of 1:
We have given a quadratic equation 3![x to the power of 2 end exponent plus 6 x plus 8 equals 0](data:image/png;base64,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)
![b to the power of 2 end exponent minus 4 a c equals open parentheses 6 close parentheses to the power of 2 end exponent minus 4 blank cross times blank 3 blank cross times blank 8](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANIAAAASCAYAAAAucYD2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA+hJREFUeNrtW1FkXEEUfVZFVC1VUREVKiLyESGiIqJCvyIqQlT0oyJERVRV6UdUVZVVVZW/qqp+VInKR0WEqFgRESIqH1Gh+lFRlb8VEWvZ3tueV2/H3WT27XtvZrtzOGTfzuzeuXPvzLkzG8+rHEUwT1wntnkOccD5uU6QIk4Tt50rnJ8dqsexc0EJOOgzFbTPoI/zcx3jKjHr3PAPXcSNEP3W0df5+T/BEaSEDpoRAJcTsGsY9YLtYH90C897ifPEHHaWT0gOHz3ENefnPxgkLiEW2Vd7xJfEC4btOkucIx7CrmVii9SQi9kdzQ9tJy5ikuPGOeJuDSRSNwJexRQSpx2v08SbQuKsIaHq3c+rxFFig+LbZcN2vSE+JZ6BbSzJN6WGI8QPmjvREgIiCbwiTtZAIj0jzijPOolbmv3vKLWV83MpcpadBbByy0sNHxFniY+JP9FxVVgNeXI7EjK+n/gZf5eb4BRs/oWBfSG2lllxOdj30W6BeD5CW3nFHBCCc1yzf19grDb6+STMgpW+pwuWtV8N23SIGArG3Q+pIWv4b8QHCDBu+ELYpYoC40ADpGbrKRO8CO3q2zyP3VVNom1szWl89n3UBJ7G+HTGm1PkiIfJb65gvDmL/RwmcKtNoovECdRJQ4ZtmoNqCC58z6WGe5AiQaQNbqkZRSpJEzyOxAnineD0DBwRJwpl5EA7dr8j7IRbqJEk5C31c5jArSaJ1AXkrgU2dWF+mFmotgFJHh0JnRurTKSwq3uXULgXyxSmfcqzrCLteGwHEcs43UQqYiccQpGagoziRWs6wkSK28+VBu5KBHLOw5yNoKi/atAmjqf3UBe+6uiBgiu5triCoDxNtycFdlybxgSrx/UpaNkger3yR8tRBqUk7fiZdETajVrtJGlnk59NJVJQmm8atGnBk+/5BtW8YYn0Vmh4j/jQQCLpBvKBUDSrP6UZgiPixgq+Xz2YSWnKOBOLVpgFIwkZpXNqlqRNx7rvzaGok4rQZs8OSBO7D/npg5P+o9KmJ8SJTxhIx98s324IbTuEFXYGn2Gjn00dNgQl6J5Bm3Y9+UfDnaiVSrYuNvQaXrfg2YRnD6QJfuL9PWJOBXTsktCOj8T9y7Q0itf+iO2TLmQbULNN4rt9Gb0T8LUP6UK2VhIpyqNm9tdYoKZk+fSdeMugTaNIpkHY5NvFNdLtYEO+g7mOZCog8EY8u1A8wSnz2I0aMRbV9kuYoAKCeDImGzcELd1EfI3arQA7BoRdc81yPycF9s0iJJN/lzlsgV/GUDbkYVfWwhyJFE0GvzuuH606ONQdeKuv5N8ouC6acm6rbfwGbDlIKMhgCb4AAAFXdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPmI8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPi08L21vPjxtbj40PC9tbj48bWk+YTwvbWk+PG1pPmM8L21pPjxtbz49PC9tbz48bXN1cD48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bW4+NjwvbW4+PC9tZmVuY2VkPjxtbj4yPC9tbj48L21zdXA+PG1vPi08L21vPjxtbj40PC9tbj48bWk+JiN4QTA7PC9taT48bW8+JiN4RDc7PC9tbz48bWk+JiN4QTA7PC9taT48bW4+MzwvbW4+PG1pPiYjeEEwOzwvbWk+PG1vPiYjeEQ3OzwvbW8+PG1pPiYjeEEwOzwvbWk+PG1uPjg8L21uPjwvbWF0aD7XiKzAAAAAAElFTkSuQmCC)
![equals 36 minus 96](data:image/png;base64,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)
![equals negative 60 less than 0](data:image/png;base64,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)
The discriminant is less than zero, so it has no real solutions.
The discriminant is the part of the quadratic formula found within the square root.