Advertisements
Advertisements
प्रश्न
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
kx2 + 2x + 3k = 0
Advertisements
उत्तर
kx2 + 2x + 3k = 0.
Here, a = k, b = 2, and c = 3k.
Sum of roots = `-b/a = -(2)/k`
Product of root = `c/a`
= `(3k)/k`
= 3
Sum of roots = Product of roots
`-(2)/k = 3`
⇒ 3k = -2
⇒ k = `-(2)/(3)`.
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x2 + (p – 3)x + p = 0.
Which of the following equations has no real roots?
The roots of quadratic equation x2 – 1 = 0 are ______.
The roots of quadratic equation x(x + 8) + 12 = 0 are ______.
