Advertisements
Advertisements
प्रश्न
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
Advertisements
उत्तर
The given quadratic equation is
kx2 + 6x - 3k = 0
Here, a = k, b = 6 and c = -3k
Sum of the roots α + β = `(-b)/a = (-6)/k`
and product of the roots αβ = `c/a = (-3k)/k`
Since, Sum of the roots = product of the roots
⇒ `(-6)/k = -3`
⇒ k = `(+6)/(+3)`
⇒ k = 2.
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in the following quadratic equation:
k2x2 – 2(2k – 1)x + 4 = 0
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
Find the value of k for which the roots of the equation 3x2 – 10x + k = 0 are reciprocal of each other.
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
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.
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
Find the values of p for which the equation 3x2 – px + 5 = 0 has real roots.
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
