Determine the value of k so that the two roots of the equation x 2- kx -36-0 are equal-A- - 12B- - 14C- - 10D- - 11

The correct option is A ± 12We know that the roots of a quadratic nbsp;equation ax^2+bx+c=0 are equal when nbsp;D = 0. i.e., b^2 4ac=0 For equation nbsp ...

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Standard X

Mathematics

Nature of Roots

Determine the...

Question

Determine the value of k so that the two roots of the equation x² − kx + 36 = 0 are equal.

\pm 12

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Solution

The correct option is A $\pm 12$
We know that the roots of a quadratic equation $a x^{2} + b x + c = 0$ are equal when D = 0.
i.e., $b^{2} - 4 a c = 0$

For equation x² − kx + 36 = 0,
a = 1, b = -k and c = 36

$\Rightarrow (- k)^{2} - (4 \times 1 \times 36) = 0$
$\Rightarrow k^{2} - 144 = 0$
$\Rightarrow k^{2} = 144$
$∴ k = 12 or - 12$

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Determine the value of k so that the two roots of the equation x2 − kx + 36 = 0 are equal.

The correct option is A ±12We know that the roots of a quadratic equation ax2+bx+c=0 are equal when D = 0. i.e., b2−4ac=0 For equation x2 − kx + 36 = 0, a = 1, b = -k and c = 36 ⇒(−k)2−(4×1×36)=0 ⇒k2−144=0 ⇒k2=144 ∴k=12 or −12

Determine the value of k so that the two roots of the equation x² − kx + 36 = 0 are equal.