Sachin and Rahul solve a quadratic equation. | vedclass

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(B) Let the quadratic equation be $x^2 + bx + c = 0$.Sachin made a mistake in the constant term $c$,so his roots $(4, 3)$ are correct for the coeffici

Vedclass · Accepted Answer

$6, 1$

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(B) Let the quadratic equation be $x^2 + bx + c = 0$.Sachin made a mistake in the constant term $c$,so his roots $(4, 3)$ are correct for the coefficient $b$. The sum of roots is $-(b) = 4 + 3 = 7$,so $b = -7$.Rahul made a mistake in the coefficient $b$,so his roots $(3, 2)$ are correct for the constant term $c$. The product of roots is $c = 3 	imes 2 = 6$.The correct quadratic equation is $x^2 - 7x + 6 = 0$.Factoring the equation: $x^2 - 6x - x + 6 = 0 \implies x(x - 6) - 1(x - 6) = 0 \implies (x - 6)(x - 1) = 0$.The correct roots are $x = 6$ and $x = 1$.

Sachin and Rahul solve a quadratic equation. Sachin makes a mistake in writing the constant term and obtains roots $(4, 3)$. Rahul makes a mistake in writing the coefficient of $x$ and obtains roots $(3, 2)$. What are the correct roots of the equation?

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