Question

Write the set of value of k for which the quadratic equations has 2x² + kx − 8 = 0 has real roots.

Answer 1

SOLUTION :  

Given : 2x² + kx - 8 = 0

On comparing the given equation with ax² + bx + c = 0  

Here, a = 2 , b = k , c = - 8

D(discriminant) = b² – 4ac

D = k² - 4 × 2 × ( -8)

D = k² + 64

D = k² + 64 ≥ 0

Given equation has real roots , i e D ≥ 0

Since, k² + 64 ≥ 0

Hence, for all real value of ‘k’  the given equation has real roots.

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Answer 2

the given equation has real roots,
a = 2 ,
b = k
c = 8.
D = 0 b2 - 4ac
= 0 k2 - 4 * 2 *8
= 0 k2
= 64 k
= ± √64
∴k = ± 8.