Question

For what value of k, the quadratic polynomial kx² + x + k has equal zeroes ?​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ kx² + x + k = 0.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

⇒ For equal roots : D = 0.

⇒ (1)² - 4(k)(k) = 0.

⇒ 1 - 4k² = 0.

⇒ 1 = 4k².

⇒ k² = 1/4.

⇒ k = √1/4.

⇒ k = ± 1/2.

                                                                                                                           

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

Question:-

• For what value of k, the quadratic polynomial kx² + x + k has equal zeroes ?

To Find:-

• Find the value of k.

Solution:-

We have to find the value of k:-

$\sf\longrightarrow \: { b }^{ 2 } - 4ac = 0$

$\sf\longrightarrow \: { 1 }^{ 2 } - 4( k )( k ) = 0$

$\sf\longrightarrow \: 4 { k }^{ 2 } = 1$

$\sf\longrightarrow \: { k }^{ 2 } = \dfrac { 1 } { 4 }$

$\sf\longrightarrow \: k = \sqrt { \dfrac { 1 } { 4 } }$

$\sf\longrightarrow \: k = \dfrac { 1 } { 2 }$