Advertisements
Advertisements
Question
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Advertisements
Solution
16x2 - 40x + 25 = 0
a = 16, b = -40, c = 25
∴ D = b2 - 4ac
= (-40)2 - 4 x 16 x 25
= 1600 - 1600
= 0
∴ Discriminant = 0
∵ D = 0
∴ Roots are real and equal.
APPEARS IN
RELATED QUESTIONS
Find the value of p for which the quadratic equation (2p + 1)x2 − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.
If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2 (ac + bd) x + (c2 + d2) = 0 has no real roots.
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 2x + 1 = 0
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
