(A) Let the roots of the quadratic equation $x^2-35x+c=0$ be $2t$ and $3t$. Sum of the roots $= 2t + 3t = -(-35)/1 = 35$. $5t = 35 \Rightarrow t = 7$.

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(A) Let the roots of the quadratic equation $x^2-35x+c=0$ be $2t$ and $3t$. Sum of the roots $= 2t + 3t = -(-35)/1 = 35$. $5t = 35 \Rightarrow t = 7$. Product of the roots $= (2t)(3t) = c/1 = c$. $6t^2 = c$. Since $t = 7$,$c = 6(7^2) = 6 \times 49$. Given $c = 6K$,we have $6K = 6 \times 49$. Therefore,$K = 49$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Relation between roots and coefficients

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If the roots of the quadratic equation $x^2-35x+c=0$ are in the ratio $2:3$ and $c=6K$,then $K=$

AP EAMCET 2024 All AP EAMCET

A
$49$
B
$14$
C
$21$
D
$7$

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4-2.Quadratic Equations and Inequations

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