Question

find the valus of k
2x2 + kx + 3 = 0 ​

Answer 1

Question:

Find the values of k so that the polynomial has two equal roots.

$2x^{2} + kx + 3 = 0$

Solution:

In the given polynomial,

a = 2

b = k

c = 3

Roots are equal here,

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

$b^{2} - 4ac = 0 \\ k^{2} - 4(2)(3) = 0 \\ k^{2} = 24 \\ k = \pm\sqrt{24}$

Therefore, the values of k are $-\sqrt{24}$ and $+\sqrt{24}$

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

To find :- The value of "k".

General form of quadratic equation is ax² + bx + c = 0.

A quadratic equation ax² + bx + c = 0 has :-

i) two distinct real roots, if b²-4ac >0.

ii) two equal roots, if  b²-4ac = 0 and

iii) no real roots, if  b²- 4ac <0.

2x² + kx + 3 = 0 ​

a = 2

b = k

c = 3

Since, the equation has two equal roots.,

b²- 4ac = 0

Now Put the values in it.

k² - 4 × 2 × 3 = 0

k² - 24 = 0

k² = 24

k = ±√24

$\huge{\boxed{\sf{Hence\:the\:value\:of\:k\:=\:\pm\:\sqrt{24}}}}$