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
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Determine whether the given values of x is the solution of the given quadratic equation below:
6x2 - x - 2 = 0; x = `(2)/(3), -1`.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax2 + bx + c = 0 is:
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
