Question

If the equation 2 x² - 7 x + 1 = 0 and ax² + bx + 2 = 0
common root, then
(a) a = 2, b = -7 (b) a = -(7/2), b = 1
(b) a = 4, b = 1 (d) none of these

Answer 1

Question:

If the equations 2 x²-7 x+1 = 0 and ax²+bx+2 = 0

common root, then

(a) a = 2, b = -7

(b) a = -(7/2), b = 1

(b) a = 4, b = 1

(d) none of these

Answer:

d). None of these

Note:

• If two equations have all the roots in common, then both the equations are equivalent.

• If the two quadratic equations ax² + bx + c = 0 and Ax² + Bx + C = 0 are equivalent , then ;

a/A = b/B = c/C .

Solution:

Here ,

It is given that , the given quadratic equations

2x² - 7x + 1 = 0 and ax² + bx + 2 = 0 have common roots.

Since,

They have common roots , hence they are equivalent.

Thus,

2/a = -7/b = 1/2

If 2/a = 1/2

=> a/2 = 2

=> a = 2•2

=> a = 4

If -7/b = 1/2

=> b/-7 = 2

=> b = -7•2

=> b = -14

Hence,

The required value of the a and b are 4 and -14 respectively.

Answer 2

Given equation:

x² - 7 x + 1 = 0 and ax² + bx + 2 = 0

Solution:

We know that If the two quadratic equations ax² + bx + c = 0 and Ax² + Bx + C = 0 are equivalent , then a/A = b/B = c/C .

Since the given equations are equivalent (having common roots) We have,

2/a = -7/b = 1/2

when 2/a = 1/2

=> a/2 = 2

=> a = 2 × 2

=> a = 4

Also when -7/b = 1/2

=> b/-7 = 2

=> b = -7 × 2

=> b = -14

Hence,The required values of a and b are 4 and -14 respectively.