Question

If one zero of the quadratic polynomial 2x2 – (k2 +k-12) x +3 =0 is additive inverse of the

other. Then find k.​

Answer 1

$Given \: Quadratic \: equation :$

$2x^{2} - (k^{2} + k - 12)x + 3 = 0$

$Compare \:this \: with \: ax^{2}+bx+c=0 , we\\get$

$a = 2 , b = -(k^{2} + k - 12)\:and \: c = 3$

/* According to the problem given */

$Let \: \alpha \:and \: - \alpha \: are \:two \\zeroes \: of \: the \: equation$

$Sum \:of \: the \: Zeroes = \frac{-b}{a}$

$\implies \alpha + ( -\alpha ) = \frac{-[-(k^{2}+k-12)]}{2}$

$\implies 0 = \frac{(k^{2}+k-12)]}{2}$

$\implies k^{2}+k-12=0$

/* Splitting the middle term, we get */

$\implies k^{2} +4x-3x-12 = 0$

$\implies k(k+4) - 3(x+4) = 0$

$\implies (k+4)(k-3) = 0$

$\implies k+4 = 0 \:Or \: k-3 = 0$

$\implies k = -4 \:Or \:k = 3$

Therefore.,

$\green { k = -4 \:Or \:k = 3}$

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