Question

2
3.
The roots of ax2 b + c = 0 are greater
than the roots of 2x2 + 3x + 1 = 0 by unity,
then
(1) 262 = a (1 + 4ac)
(2) 262 = a2(1 + Bac)
(3) 8b2 = a (1 + 4ac)
(4) 4b2 = a (1 + 16ac)​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The roots of ax² + bx + c = 0 are greater than the roots of 2x² + 3x + 1 = 0 by unity, then

(1) 2b² = a (1 + 4ac)

(2) 2b² = a²(1 + 8ac)

(3) 8b² = a (1 + 4ac)

(4) 4b² = a (1 + 16ac)

EVALUATION

Here the given equation is

2x² + 3x + 1 = 0

Now the equation whose roots are greater than the roots of 2x² + 3x + 1 = 0 by unity is obtained as below

$\sf{2 {(y + 1)}^{2} + 3(y + 1) + 1 = 0}$

$\sf{ \implies \: 2 {y}^{2} + 7y + 6 = 0}$

If we express in terms of the variable x then we get the equation as

$\sf{ \: 2 {x}^{2} + 7x + 6 = 0}$

Now Comparing with the equation ax² + bx + c = 0 we get

a = 2 , b = 7 , c = 6

Now 2b² = 2 × 7² = 2 × 49 = 98

a (1 + 4ac)

= 2 × ( 1 + 4 × 2 × 6 )

= 2 × 49

= 98

∴ 2b² = a (1 + 4ac)

FINAL ANSWER

Hence the correct option is

(1) 2b² = a (1 + 4ac)

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. find the equation that formed by increasing each root of 2x²-3x-1=0by 1

https://brainly.in/question/33063519

2. find the equation that formed by squaring each root of the equation x²+3x-2=0

https://brainly.in/question/33064705