Question

The value of k for which the quadratic equation  kx²– 3kx + 4 = 0 has equal roots is​

Answer 1

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equation :- kx² - 3kx + 4 = 0

given :- equation have equal roots

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${kx}^{2} - 3kx + 4 = 0$

we know that if the roots of a quadratic equation is equal then..

Discriminant = 0

$d = {b}^{2} - 4ac$

$\implies \: {(3k)}^{2} + 4 \times 4 \times k = 0 \\ \implies \: 9 {k}^{2} + 16k = 0 \\ \implies \: k(9k + 16) = 0 \\ \implies \: 9k + 16 = \frac{0}{k} \\ \implies \: 9k + 16 = 0 \\ \implies \: 9k = - 16 \\ \implies \: k = \frac{ - 16}{9}$

hence, value of k is -16/9

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quadratic equation is in the form ax²+bx+c = 0

quadratic formula:-

$x = \frac{ - b \: ± \: \sqrt{d} }{2a}$

where,

$discriminant \ \:( d )= {b}^{2} - 4ac$

• if discriminant = 0

then roots are real and equal

• if discriminant > 0

then roots are real and distinct

• if discriminant < 0

then real roots does not exist