If the sum of the roots of the equation 3x 2 – (3k – 2) x – (k – 6) = 0 is equal to the product of its roots then k = ?

Question

Philoid · Accepted Answer

Let the roots of the given quadratic equation 3x² – (3k – 2)x – (k – 6)=0 be α and β.

Now,

sum of roots = α + β = (3k – 2)/3 and,

product of roots = αβ = – (k – 6)/3

[∵ If α and β are the roots of quadratic equation ax² + bx + c=0 then α + β = – b/a and αβ = c/a]

According to question –

sum of roots = product of roots

∴ α + β = αβ

⇒ (3k – 2)/3 = – (k – 6)/3

⇒ 3k – 2 = – k + 6

⇒ 4k = 8

∴ k = 2

Hence, The value of k is 2.