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 each of the following equation:
(3k+1)x2 + 2(k + 1)x + k = 0
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
`10x -(1)/x` = 3
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
If (1 – p) is a root of the equation x2 + px + 1 – p = 0, then roots are:
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
