Question

If a and b are zeroes of 2x² + 5x + k find the value of k such that (a+b)²-ab = 24
answer is -71/2​

Answer 1

Given :

• α and β are zeroes of 2x² + 5x + k.
• (α + β)² - αβ = 24

To find :

• Value of k =?

Formula Used :

• f(x) = ax² + bx + c.
• Sum of roots = -b/a
• Product of roots = c/a

Step-by-step explanation :

2x² + 5x + k

a = 2

b = 5

c = k

f(x) = ax² + bx + c

Sum of roots, α + β = -b/a = - 5/2

Product of roots, αβ = c/a = k/2

According to the question,

(α + β)² - αβ = 24

(-5/2)² - k/2 = 24

25/4 - k/2 = 24

25 - 2k/4 = 24

25 - 2k = 24 × 4

25 - 2k = 96

-2k = 96 - 25

-2k = 71

k = 71/-2

Or, k = - 71/2

Therefore, Value of k = - 71/2.