Question

Value of k for which the quadratic equation 2x^2+Kx+2=0 have no real roots.

A. k<4
B. k=4
C. k>4
D. k>16 ​

Answer 1

Answer

The correct option is (A) k < 4

Given

The quadratic equation is

• 2x² + kx + 2 = 0

To Find

• The value of k

Solution

We are given,

The quadratic equation

2x² + kx + 2 = 0 has no real root

This refers that its discriminant ,

b² - 4ac < 0

Here , in the equation :

a = 2 , b = k and c = 2

Thus ,

$\longrightarrow \sf b {}^{2} - 4ac < 0 \\ \\ \sf\implies {k}^{2} - 4 \times 2 \times 2 < 0 \\ \\ \sf \implies {k}^{2} - 16 < 0 \\ \\ \sf \implies {k}^{2} < 16 \\ \\ \sf \implies k {}^{2} < {4}^{2} \\ \\ \sf \implies k < 4$

Thus the value of k is less than 4 ( k < 4)

Answer 2

SOLUTION :

$\bigstar$ Firstly, we know that formula of discriminant for no real roots.

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

Given, quadratic equation : 2x² + kx + 2 = 0

As we know that compared with ax² + bx + c;

• a = 2
• b = k
• c = 2

Now;

$\longrightarrow\sf{(k)^{2} -4\times 2\times 2<0}\\\\\longrightarrow\sf{k^{2} -16<0}\\\\\longrightarrow\sf{k^{2} <16}\\\\\longrightarrow\sf{k<\sqrt{16} }\\\\\longrightarrow\bf{k<4}$

Option (A).