Advertisements
Advertisements
प्रश्न
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
Advertisements
उत्तर
x2 – (m + 2)x + (m + 5) = 0
Here a = 1, b = – 4(m + 2) and c = m + 5
Given equation has equal roots
Then D = 0
`=>` b2 – 4ac = 0
`=>` [–(m + 2)]2 – 4(1)(m + 5) = 0
`=>` m2 + 4m + 4 – 4m – 20 = 0
`=>` m2 – 16 = 0
`=>` m2 = 16
`=>` m = ±4
Put value of m in given equation
x2 – 6x + 9 = 0 or x2 + 2x + 1 = 0
`=>` (x – 3)2 = 0 or (x + 1)2 = 0
`=>` x – 3 = 0 or x + 1 = 0
`=>` x = 3 or x = –1
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`(x+3)/(x+2)=(3x-7)/(2x-3)`
Solve each of the following equations by factorization:
`9/2x=5+x^2`
Solve the following quadratic equations by factorization:
\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11; x \neq \frac{3}{5}, - \frac{1}{7}\]
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
If p and q are the roots of the equation x2 – px + q = 0, then ______.
The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.
Solve the following by reducing them to quadratic form:
`sqrt(y + 1) + sqrt(2y - 5) = 3, y ∈ "R".`
In each of the following determine whether the given values are solutions of the equation or not.
x2 + x + 1 = 0; x = 1, x = -1.
Harish made a rectangular garden, with its length 5 metres more than its width. The next year, he increased the length by 3 metres and decreased the width by 2 metres. If the area of the second garden was 119 sq m, was the second garden larger or smaller ?
