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Nature of Roots

x2-m-3x+m=0 m...

Question

$x^{2} - (m - 3) x + m = 0 (m \in R)$ be a quadratic equation. Find the value of $m$ for which both the roots are equal:

{1, 9}

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0

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3

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{4, 11}

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Solution

The correct option is A ${1, 9}$
Both roots are equal $\Rightarrow b^{2} = 4 a c$

$\Rightarrow (m - 3)^{2} = 4 m$

$\Rightarrow m^{2} - 10 m + 9 = 0$

$\Rightarrow (m - 1) (m - 9) = 0$

$\Rightarrow m = 1$ or $m = 9$

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