Question

find the value of k so that equations 15 X square + kx + 15 is equal to zero and X square + X + K equal to zero has simultaneously real roots​

Answer 1

Step-by-step explanation:

A quadratic equation is said to have equal roots if its discriminant is equal to zero.

Discriminant is a equation which is calculated based on the coefficients of the terms in a quadratic equation. There are three cases to define nature of roots for a given quadratic equation.

-D > 0

-D = 0

-D < 0

-D is the discriminant which is written as: b² - 4ac

Here,

'a' is the coefficient of x²

'b' is the coefficient of x

'c' is the constant term

E.g. : x² - 5x + 6

Here, a = 1 ; b = 5 ; c = 6

Coming to your question,

Given quadratic equation: kx² + ( 2k + 4 ) x + 9 = 0

From this we get,

a = k

b = 2k + 4

c = 9

Substituting them in the equation of discriminant we get,

→ ( 2k + 4 )² - 4 ( k ) ( 9 )

→ 4k² + 16k + 16 - 36k

→ 4k² - 20k + 16

Since the question says the equation has equal roots, we equate the above D to zero. Hence we get,

→ 4k² - 20k + 16 = 0

→ 4k² - 4k - 16k + 16 = 0

→ 4k ( k - 1 ) - 16 ( k - 1 ) = 0

→ ( 4k - 16 ) ( k - 1 ) = 0

→ k = 4, 1

Therefore the given equation can have 'k' value as 1 as well as 4.