You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Nature of Roots

Find the numb...

Question

Find the number of $a$ for which given equation have equal roots $x^{2} + 3 x - (a^{2} + a - 2) = 0$

Open in App

Solution

$x^{2} + 3 x - (c^{2} + a - 2) = 0$
For roots to be equal,
$b^{2} + 4 a c = 0$
$9 + 4 (a^{2} + a - 2) = 0$
$⟹ a^{2} + a - 2 = \frac{- 9}{4}$
$⟹ a^{2} + a + \frac{1}{4} = 0$
$⟹ 4 a^{2} + 4 a + 1 = 0$
$⟹ 4 a^{2} + 2 a + 2 a + 1 = 0$
$⟹ 2 a (2 a + 1) + 1 (2 a + 1) = 0$
$⟹ a = \frac{- 1}{2}$

Suggest Corrections

Similar questions

Q. For what values of

a

does the equation

x^{2} + 2 a \sqrt{a^{2} - 3} x + 4 = 0

possess equal roots?

Q. Number of values of

a

for which given equation have equal roots

x^{2} - 2 x - (4 a^{2} - 16 a + 15) = 0

Q. Without solving the following quadratic equation, find the greater value of

p

for which the given equation has real and equal roots.

x^{2} + (p - 3) x + p = 0

Q. Find the values of

k

for which the given equation has real and equal roots

2 x^{2} + 3 x + k = 0

Q. Choose the correct answers for the following questions.
(1) Which one is the quadratic equation ?

(A)

\frac{5}{x} - 3 = x^{2}

(B) x(x + 5) = 2

(D)

\frac{1}{x^{2}} (x + 2) = x

(2) Out of the following equations which one is not a quadratic equation ?

(A) x² + 4x = 11 + x²

(B) x² = 4x

(D) 2x – x² = x² + 5

(3) The roots of x² + kx + k = 0 are real and equal, find k.

\sqrt{2} x^{2} - 5 x + \sqrt{2} = 0

find the value of the discriminant.

(A) –5

(B) 17

(C)

\sqrt{2}

(D)

2 \sqrt{2} - 5

(5) Which of the following quadratic equations has roots 3,5 ?

(A) x² – 15x + 8 = 0	(B) x² – 8x + 15 = 0
(C) x² + 3x + 5 = 0	(D) x² + 8x – 15 = 0

(6) Out of the following equations, find the equation having the sum of its roots –5.

(A) 3x² – 15x + 3 = 0	(B) x² – 5x + 3 = 0
(C) x² + 3x – 5 = 0	(D) 3x² + 15x + 3 = 0

(7)

\sqrt{5} m^{2} - \sqrt{5} m + \sqrt{5} = 0

which of the following statement is true for this given equation ?

(A) Real and uneual roots	(B) Real and equal roots
(C) Roots are not real	(D) Three roots.

(8) One of the roots of equation x² + mx – 5 = 0 is 2; find m.

(A) –2

(B)

- \frac{1}{2}

(C)

\frac{1}{2}

(D) 2

Join BYJU'S Learning Program

Find the number of a for which given equation have equal rootsx2+3x−(a2+a−2)=0

x2+3x−(c2+a−2)=0For roots to be equal,b2+4ac=09+4(a2+a−2)=0⟹a2+a−2=−94⟹a2+a+14=0⟹4a2+4a+1=0⟹4a2+2a+2a+1=0⟹2a(2a+1)+1(2a+1)=0⟹a=−12

Find the number of $a$ for which given equation have equal roots $x^{2} + 3 x - (a^{2} + a - 2) = 0$