Advertisements
Advertisements
प्रश्न
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
Advertisements
उत्तर
The equation (x + 4)2 – 8x = 0 has no real roots.
Simplifying the above equation,
x2 + 8x + 16 – 8x = 0
x2 + 16 = 0
D = b2 – 4ac
= (0) – 4(1)(16) < 0
Hence, the roots are imaginary.
APPEARS IN
संबंधित प्रश्न
Find that value of p for which the quadratic equation (p + 1)x2 − 6(p + 1)x + 3(p + 9) = 0, p ≠ − 1 has equal roots. Hence find the roots of the equation.
Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.
px2 – 4x + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + 4x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Solve the following quadratic equation using formula method only
`3"x"^2 - 5"x" + 25/12 = 0 `
Solve the following quadratic equation using formula method only
`"x"^2 - 4 sqrt 15 "x" - 4 = 0`
Find the values of k for which each of the following quadratic equation has equal roots: x2 – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is:
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
If α + β = 4 and α3 + β3 = 44, then α, β are the roots of the equation:
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
The roots of quadratic equation x(x + 8) + 12 = 0 are ______.
