Question

If a and b are the roots of the equation x²+ax-b=0 then find a and b.

Answer 1

SOLUTION :  

Option (d) is correct : - 1

Given : ‘a’ & 'b’ are the roots of the equation x² + ax + b = 0

On comparing the given equation with ax² + bx + c = 0  

Here, a = 1 , b = a  , c = b

Sum of zeroes = - b/a  

a + b  = - b/a

a + b  = - a/1

a + b  = - a

b = - a - a

b = - 2a ………..(1)

Product of zeroes = c/a  

a × b = c/a

ab = b/1

ab = b

a = b/b  

a = 1

On putting the value of a = 1 in eq 1

b = - 2a

b = - 2(1)

b = - 2

The value of a + b = 1 + (- 2)

a + b = 1 - 2  

a + b = - 1

Hence, the value of (a + b) is - 1.

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Answer 2

Given:

• a and b are the roots of the equation $x^2+ax-b=0$

To Find:

• The value of a and b.

Solution:

Let $x^2+ax-b=0$  → (equation 1) and $Ax^2+Bx-C=0$ → (equation 2)

On comparing equation 1 and equation 2 we get,

A = 1, B = a, and C = -b

⇒ Sum of the roots = a+b = -B/A ( on substituting the values we get)

⇒ a+b = -a/1 = -a

⇒ product of the roots = ab = C/A   ( on substituing the values we get)

⇒ ab = -b/1 = -b

Consider sum of the roots,

⇒ a+b = -a  ( on solving we will get the value of 'b' in terms of 'a')

⇒ b = a+a = 2a

∴ b = 2a → (equation 3)

Now consider product of the roots,

We need to find the value of 'a' using this equation inorder to find the value of 'b'.

⇒ ab = -b

⇒ a = -b/b = -1

∴ a = -1

Substitute the value of 'a' in equation 3.

∴ equation 3 becomes,

b = 2(-1) = -2

∴ a = -1 and b = -2

∴ The value of a = -1 and b = -2