Question

Find the value(s) of k for which the equation (x)^2 + 5kx + 16 = 0 has real and equal roots.

Answer 1

Answer:

Answer:

Equation: x² + 5kx + 16 = 0

It is given that all the roots are equal.

For roots to be equal, the value of Discriminant must be equal to zero.

=> D = b² -4ac

a = 1, b = 5k, c = 16

=> D = ( 5k )² - 4 ( 1 ) ( 16 )

=> D = 25 k² - 64  

We know that D is equal to zero.

=> 25k² - 64 = 0

=> 25k² = 64

=> k² = 64 / 25

=> k = √ ( 64 / 25 )

=> k = + 8 / 5 ( or ) - 8 / 5

Hope it helped !!

Answer 2

Answer:

$\large\bf\underline\red{Question ➡} \\ \\ \sf \: find \: the \: value \: of \: k \: for \: which \: the \: \\ \sf \: equation \: {x}^{2} + 5kx + 16 = 0 \: has \\ \sf \: an d\: equal \: roots \\ \\ \large\bf\underline\red{solution➡} \\ \\ \bf \underline{ for \: equal \:roots \: and \: real \: root : } \\ \\ \fbox\red{ b² \: - \: 4ac = 0 } \\ \\ \sf {(5k)}^{2} - 4 \times 1 \times 16 = 0 \\ \\ \sf \: 25 {k}^{2} - 64 = 0 \\ \\ \sf 25 {k}^{2} = 64 \\ \\ \sf \: {k}^{2} = \frac{64}{25} \\ \\ \sf k = \sqrt{ \frac{64}{25} } \\ \\ \large{\boxed{\mathtt\red{\fcolorbox{magenta}{aqua}{k = 8/5}}}}$