Advertisements
Advertisements
Question
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
2x2 - (3k + 1)x - k + 7 = 0.
Solution
2x2 - (3k + 1)x - k + 7 = 0
Here,
a= 2,
b = -(3k + 1)
c = -k + 7
Sum of roots = `(-b)/a`
= `(3k + 1)/(2)`
Product of roots = `c/a`
= `(-k + 7)/(2)`
Sum of roots = Product of roots
`(3k + 1)/(2) = (-k + 7)/(2)`
6k + 2 = -2k + 14
8k = 12,
⇒ k = `(12)/(8)`
∴ k = `(3)/(2)`.
APPEARS IN
RELATED QUESTIONS
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 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.
Every quadratic equation has exactly one root.
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal. Prove that: 2q = p + r, that is, p, q and r are in A.P.
Equation 2x2 – 3x + 1 = 0 has ______.
