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प्रश्न
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
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उत्तर
Given quadratic equation is (m + 4)x2 + (m + 1)x + 1 = 0
The quadratic equation has real and equal roots if its discriminant is zero.
`=>` D = b2 – 4ac = 0
`=>` (m + 1)2 – 4(m + 4)(1) = 0
`=>` m2 + 2m + 1 – 4m – 16 = 0
`=>` m2 – 2m – 15 = 0
`=>` m2 – 5m + 3m – 15 = 0
`=>` m(m – 5) + 3(m – 5) = 0
`=>` (m – 5)(m + 3) = 0
`=>` m = 5 or m = –3
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
5x2 - 4x + 2 + k(4x2 - 2x - 1) = 0
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Find the values of k for which each of the following quadratic equation has equal roots: x2 – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax2 + bx + c = 0 is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
