Advertisements
Advertisements
Question
If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.
Solution
Given that, b = 0 and c < 0 and quadratic equation,
x2 + bx + c = 0 .....(i)
Put b = 0 in equation (i), we get
x2 + 0 + c = 0
⇒ x2 = – c ......`[("Here" c > 0),(therefore - c > 0)]`
∴ x = `+- sqrt(-c)`
So, the roots of x2 + bx + c = 0 are numerically equal and opposite in sign.
APPEARS IN
RELATED QUESTIONS
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Without solving, examine the nature of roots of the equation 2x2 + 2x + 3 = 0
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Find the value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
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:
kx2 + 2x + 3k = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
The roots of quadratic equation x2 – 1 = 0 are ______.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
