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
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
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
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
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
15x2 - 28 = x
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Find the values of p for which the equation 3x2 – px + 5 = 0 has real roots.
Choose the correct answer from the given four options :
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are
Which of the following equations has no real roots?
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
If one root of the quadratic equation 2x2 + kx – 6 = 0 is 2, the value of k is:
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
If one root of equation (p – 3) x2 + x + p = 0 is 2, the value of p is ______.
Which of the following equations has imaginary roots?
