Question

Find the value of k for which the roots of the quadratic equation 2x2+kx+8=0, will have equal value.

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The roots of the quadratic equation 2x² + kx + 8 = 0 will have equal value.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The value of k.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We have 2x² + kx + 8 = 0

A/q

Discriminate (D) = 0

• a = 2
• b = k
• c = 8

Formula use :

$\boxed{\bf{b^{2}-4ac=0}}}$

$\longrightarrow\sf{b^{2} -4ac=0}\\\\\longrightarrow\sf{(k)^{2} -4\times 2\times 8=0}\\\\\longrightarrow\sf{(k)^{2} -64=0}\\\\\longrightarrow\sf{(k)^{2} =64}\\\\\longrightarrow\sf{k=\pm\sqrt{64} }\\\\\longrightarrow\sf{\green{k=\pm8}}$

Thus;

The value of k is ±8 .

Answer 2

$\tt{\huge{\orange {-----------}}} M.V$

QUESTION :

Find the value of k for which the roots of the quadratic equation 2x2+kx+8=0, will have equal value.

SOLUTION :

According to the above question, the roots have equal and real value.

This is possible when D = 0

So we can thereby state that :

D = 0

=> D ^2 = 0

=> B^2 - 4 AC = 0

=> B^2 = 4 AC

Quadratic Equation : 2x2+kx+8=0

So,

A = 2

B = K

C = 8

B^2 = K ^2

4AC = 64

Now :

K ^2 = 64

=> K = 8 or - 8.

So, for the two values of K, 8 and - 8, the roots of the above quadratic equation, will have equal value...