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Question

Assertion :If f(x) is a quadratic polynomial satisfying f(2)+f(4)=0. If unity is a root of f(x)=0, then the other root is 72. Reason: If g(x)=px2+qx+r=0 has roots a,β,then a+β=−qp andαβ= rp.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for AssertionLet 1 and 72 are roots of f(x)=0So, sum of roots =1+72=92Product of roots =(1)72=72So, the quadratic equation is x2−92x+72=0Also, f(2)=−32f(4)=32Here, f(2)+f(4)=0Hence, our assumption is correct.72 is a root of f(x)=0Now,if f(x)=ax2+bx+c Let α,β are the roots of f(x)Then, sum of roots =α+β=−ba & product of roots =αβ=ca.Hence, assertion and reason are correct but reason is not the correct explanation for assertion

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