Question

Find the value of k for the quadratic equation 2 X square + kx + 3 equal to zero have equal roots

Answer 1

Step-by-step explanation:

Given -

• p(x) = 2x² + kx + 3 = 0 have equal roots

To Find -

• Value of k

Now,

→ 2x² + kx + 3 = 0

As we know that :-

• D = b² - 4ac = 0

→ (k)² - 4×(2)×(3) = 0

→ k² = 24

→ k = √24

→ k = 2√6

Hence,

The value of k is 2√6

Therefore,

Quadratic polynomial is 2x² + 2√6x + 3

Verification :-

→ 2x² + 2√6x + 3

By using quadratic formula :-

• x = -b ± √b² - 4ac/2a

→ -(2√6) ± √(2√6)² - 4×(2)×(3)/2(2)

→ -2√6 ± √24 - 24/4

→ -2√6 ± √0/4

Zeroes are -

→ x = -2√6/4

And

→ x = -2√6/4

Here, we see that the polynomial have equal roots and In question its given that the polynomial has equal root.

So, Our answer is absolutely correct.

Answer 2

Step-by-step explanation:

2x2+ 3x+2

d=b2 - 4ac

a=2 b=3k c= 2

3k2-4(2)(2)=0

3 k2-16 =0

3k2 =16

k=16√3