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प्रश्न
Every quadratic equation has at least two roots.
पर्याय
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
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 each of the following equation:
(2k + 1)x2 + 2(k + 3)x + (k + 5) = 0
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
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:
kx2 - 6x - 2 = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 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
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then:
(x2 + 1)2 – x2 = 0 has:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
Find whether the following equation have real roots. If real roots exist, find them.
`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`
Solve for x: 9x2 – 6px + (p2 – q2) = 0
