Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
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)`.
संबंधित प्रश्न
The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
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: `5x^2 - 6sqrt(5)x + 9` = 0
The quadratic equation whose one rational root is `3 + sqrt2` is
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.
Prove that 2q = p + r; i.e., p, q, and r are in A.P.
