For what value of k are the roots of the quadratic equation kx²+ 4x+ 1=0 equals and reals."

Question

asked Nov 21, 2022 7.9k views

1 Answer

SakisTsalk · Answer 1 · 2022-11-27T16:34:18+0000

Answer:

k ≥ 4

Explanation:

A Quadratic equation is given to us and we need to find out the value of k for which the equation has real roots. The given equation is ,

$\rm\implies kx^2 +4x +1=0$

With respect to Standard form of Quadratic equation :-

$\rm\implies ax^+bx+c=0$

For real roots ,

$\rm\implies Discriminant = b^2-4ac\geq 0$

Substitute the respective values ,

$\rm\implies b^2-4ac \geq 0\\$

$\rm\implies 4^2 - 4(k)(1) \geq 0 \\$

Simplify the LHS ,

$\rm\implies 16 - 4k \geq 0 \\$

Add 4k both sides ,

$\rm\implies 4k\geq 16$

Divide both sides by 4 ,

$\rm\implies \boxed{\blue{\rm k \geq 4}}$