Advertisements
Advertisements
Question
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
Solution
The equation (x – 1)(x + 2) + 2 = 0 has two real and distinct roots.
Simplifying the above equation,
x2 – x + 2x – 2 + 2 = 0
x2 + x = 0
D = b2 – 4ac
= 12 – 4(1)(0)
= 1 – 0 > 0
Hence, the roots are real and distinct.
APPEARS IN
RELATED QUESTIONS
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + kx + 1 = -4x2 - x
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
