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प्रश्न
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
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उत्तर
The given equation is
3x2 - 6x + 5 = 0
Here, a = 3, b = -6 and c = 5
Discriminant
= b2 - 4ac
= (-6)2 - 4 x 3 x 5
= 36 - 60
= -24 < 0
imaginary roots.
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 value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Which of the following equations has 2 as a root?
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 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`
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
