Question

if one zeroes of the quadratic polynomial (k-1)x²+kx+1 is -4then the value of k​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:k=\frac{5}{4}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {(k - 1)x}^{2} + kx + 1 = 0 \\ \\ \tt: \implies One \: zeroes = - 4 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Value \: of \: k = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies p(x) = ({k - 1)x}^{2} + kx + 1 = 0 \\ \\ \tt: \implies p( - 4) = (k - 1) { (- 4)}^{2} + k( - 4) + 1 = 0 \\ \\ \tt: \implies ( k - 1) \times 16 - 4k + 1 = 0 \\ \\ \tt: \implies 16k - 16 - 4k + 1 = 0 \\ \\ \tt: \implies 12k - 15 = 0 \\ \\ \tt: \implies 12k = 15 \\ \\ \tt: \implies k = \frac{15}{12} \\ \\ \green{\tt: \implies k = \frac{5}{4} } \\ \\ \green{\tt \therefore Value \: of \: k \: is \: \frac{5}{4} }$

Answer 2

Answer:

(k-1)x² + kx + 1 = 0

x = -4

(k - 1) (-4)² + k (-4) + 1 = 0

(k - 1) 16 - 4k + 1 = 0

16 k - 16 - 4k + 1= 0

12 k - 15 = 0

12 k = 15

k = 15/12

k = 5/4

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