Question

Find the value of k for which the equation xsquare+5kx+16=0 has equal and real roots

Answer 1

Here,
Quadratic equation is
${x}^{2} + 5kx + 16 = 0$
a = 1
b = 5k
c = 16

Equal roots means
D = 0
$= > {b}^{2} - 4ac = 0 \\ = > 25 {k}^{2} - 4 \times 1 \times 16 = 0 \\ = > 25 {k}^{2} - 64 = 0 \\ = > {(5k)}^{2} - {8}^{2} = 0 \\ = > (5k + 8)(5k - 8) = 0 \\ = > k = \frac{ - 8}{5}and \frac{8}{5}.$

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Answer 2

Answer:

X^2+5kx+16=0

For real and equal roots d=0

D=(5k)^2-4(1)(16)

0=25k^2-64

64=25k^2.

64/25=k^2.

Plus minus (√64/√25)= k

K=8/4 or k=-8/4

Step-by-step explanation: