Question

The value of K for which 2x² + 3x=k
has real and equal roots, is​

Answer 1

${2x}^{2} + 3x = k$

${2x}^{2} + 3x - k = 0$

Comparing this to the standard form of a quadratic equation

${ax}^{2} + bx + c = 0$

we get:

$a = 2 \: \: b = 3 \: \: c = - k$

It is given in the question that both the roots are equal. Hence the discriminant will also be equal to zero.

${b}^{2} - 4ac = 0$

${(3)}^{2} - (4 \times 2 \times k) = 0$

$9 - 8k = 0$

$9 = 8k$

$\frac{9}{8} = k$

Hope this helps.

Thanks.

Answer 2

Answer:

b^2 - 4ac = 0 → (1)

equation → 2x^2 + 3x - k = 0 (equation is in the form of ax^2 + bx + c = 0 )

• a = 2
• b= 3
• c = k

substituting the values of a,b,c in (1).

(3^2) - (4×2×c) = 0

9 - 8c = 0

9 = 8c

:. c = 9/8

Step-by-step explanation:

HOPE THIS HELPS YOU