Advertisements
Advertisements
Question
Choose the correct answer from the given four options :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is
Options
`(9)/(8)`
`-(9)/(8)`
`(1)/(8)`
`-(1)/(8)`
Advertisements
Solution
2x² – 5x + (k + 3) = 0
a = 2, b = –5, c = k + 3
∴ b2 – 4ac
= (–5)2 – 4 x 2 x (k + 3)
= 25 – 8(k + 3)
∴ Roots are equal.
∴ b2 – 4ac = 0
∴ 25 – 8(k + 3) = 0
25 – 8k - 24 = 0
1 – 8k = 0
⇒ 8k = 1
∴ k = `(1)/(8)`.
APPEARS IN
RELATED QUESTIONS
Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0
Solve the following quadratic equation using formula method only
5x2 - 19x + 17 = 0
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
