Advertisements
Advertisements
Question
Every quadratic equation has at least one real root.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
For example, equation x2 + 4 = 0 has no real root.
APPEARS IN
RELATED QUESTIONS
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Without solving, examine the nature of roots of the equation 2x2 – 7x + 3 = 0
If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2 (ac + bd) x + (c2 + d2) = 0 has no real roots.
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(k + 1)x + (k + 4) = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
kx2 + 6x + 1 = 0
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
ax2 + (4a2 - 3b)x - 12 ab = 0
Find the value of k for which the following equation has equal roots:
(k − 12)x2 + 2(k − 12)x + 2 = 0.
Determine whether the given values of x is the solution of the given quadratic equation below:
6x2 - x - 2 = 0; x = `(2)/(3), -1`.
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
