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प्रश्न
Every quadratic equation has at least two roots.
विकल्प
True
False
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उत्तर
This statement is False.
Explanation:
For example, a quadratic equation x2 – 4x + 4 = 0 has only one root which is 2.
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संबंधित प्रश्न
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Find the value of the discriminant in the following quadratic equation:
2x2 - 3x + 1 = O
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
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.
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
(x2 + 1)2 – x2 = 0 has:
If the difference of the roots of the equation x2 – bx + c = 0 is 1, then:
(x2 + 1)2 – x2 = 0 has ______.
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
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.
