Advertisements
Advertisements
प्रश्न
Find the value of 'p' for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
उत्तर
Given quadratic equation is
px(x – 2) + 6 = 0
`\implies` px2 – 2px + 6 = 0
For two equal and real roots
(Discriminant) D = 0
`\implies` b2 – 4ac = 0
Here, b = –2p, a = p, c = 6
∴ (–2p)2 – 4 × p × 6 = 0
`\implies` 4p2 – 24p = 0
`\implies` 4p(p – 6) = 0
`\implies` p = 6
APPEARS IN
संबंधित प्रश्न
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4 , b = ______ , c = 3
b2 – 4ac = (– 5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
A quadratic equation with integral coefficient has integral roots. Justify your answer.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
