Advertisements
Advertisements
प्रश्न
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
Advertisements
उत्तर
`3"x"^2 – 12"x" + (n – 5) = 0`
Here a = 3, b = − 12 and c = n – 5
Given: equation has equal roots
Then D = 0
⟹ `"b"^2 – 4"ac" = 0`
⟹ `[− 12]^2 – 4(3)("n" – 5) = 0`
⟹ 144 – 12n + 60 = 0
⟹ − 12n = − 204
⟹ `"n"=(-204)/-12=17`
संबंधित प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
