Advertisements
Advertisements
प्रश्न
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Advertisements
उत्तर
9a2b2x2 - 48abc + 64c2d2 = 0
Here, D = b2 - 4ac
⇒ (-48abcd)2 - 4 x 9a2b2 x 64c2d2
2304a2b2c2d2 - 2304a2b2c2d2 = 0
D = 0
Roots are real and equal.
संबंधित प्रश्न
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
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
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
In each of the following determine the; value of k for which the given value is a solution of the equation:
x2 + 2ax - k = 0; x = - a.
Discuss the nature of the roots of the following quadratic equations : x2 – 4x – 1 = 0
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 2 = 0
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
