Advertisements
Advertisements
Question
Every quadratic equation has exactly one root.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
For example, a quadratic equation x2 – 9 = 0 has two distinct roots – 3 and 3.
APPEARS IN
RELATED QUESTIONS
Solve for x : ` 2x^2+6sqrt3x-60=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(3k + 1)x + 8k + 1 = 0
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Determine whether the given values of x is the solution of the given quadratic equation below:
6x2 - x - 2 = 0; x = `(2)/(3), -1`.
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.
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.
