Sachin and Rahul attempted to solve a quadrat | vedclass

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(A) Let the quadratic equation be $ax^{2} + bx + c = 0$.Sachin made a mistake in the constant term,so the sum of the roots is correct.Sum of roots $=

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$6, 1$

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(A) Let the quadratic equation be $ax^{2} + bx + c = 0$.Sachin made a mistake in the constant term,so the sum of the roots is correct.Sum of roots $= 4 + 3 = 7$.Rahul made a mistake in the coefficient of $x$,so the product of the roots is correct.Product of roots $= 3 	imes 2 = 6$.The correct quadratic equation is $x^{2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,we get $x^{2} - 7x + 6 = 0$.Factoring the equation: $x^{2} - 6x - x + 6 = 0 \implies x(x - 6) - 1(x - 6) = 0 \implies (x - 6)(x - 1) = 0$.Thus,the correct roots are $6$ and $1$.

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up with roots $(4, 3)$. Rahul made a mistake in writing down the coefficient of $x$ and ended up with roots $(3, 2)$. The correct roots of the equation are:

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