Advertisements
Advertisements
Question
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
Solution
Given quadratic equation is x2 – ax + 1 = 0
On comparing it with ax2 + bx + c = 0, we get
a = 1, b = –a and c = 1
For real and equal roots, D = 0
i.e. b2 – 4ac = 0
⇒ (–a)2 – 4(1)(1) = 0
⇒ a2 – 4 = 0
⇒ a2 = 4
⇒ a = ±2
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 of the equation 3x2 - 10x + k = 0 are reciprocal of each other.
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
Which of the following equations has the sum of its roots as 3?
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
