Question

Out of the following, which equation has the solution x = 3.
(A) x²- 8x + 15 = 0 (B) x² + 8x - 15 = 0 (C) x²- 8x-15= 0
(D) x² + 8x - 15 = 0​

Answer 1

ANSWER : X² + 8X + 15 = 0

(Disclaimer: Your both option B & option D are same , you've a typo in the question, recheck it , option D) would be , x² + 8x + 15 )

Step-by-step solution:

Roots are real & equal when = 0

now, x² - 8x + 15 --- A

here , a = 1 , b = - 8 , c = 15

D = √b² + 4ac

D = √(- 8)² + 4 × 1 × 15

D = √64 - 60 = √4 = 2

x = - b +- √b² - 4ac / 2a

x = - 8 +- √4 / 2 × 1

x = - 8 +- 2 / 2

So either , x = -8 +2 / 2 = -6 / 2 = -3

or x = -8 -2 / 2 = -10 / 2 = -5

so value of x isn't 3 of eq A

B) x² + 8x -15 = 0

here, a = 1, b = 8 & c = -15

(They are co-efficients of variable x, (constants beside ) hope you know this)

D = √b² - 4ac

D = √8² - 4 × 1 × (-15)

D = √64 + 60 = √124 = 2√31

The value would come in decimal not 3.

so value of x isn't 3 in eq B

Perhaps you've a typo in your question as the option B) & optionD) are matching

so, option D) will be x² + 8x + 15 = 0

going by this... x² + 8x + 15 = 0

D = √b² - 4ac

D = √8² - 4 × 1 × 15 = √64 - 60 = √4 = 2

now x = -b +- √b² - 4ac / 2a

x = 8 +- √8² - 4 × 1 × 15 / 2 × 1

x = 8 +- 2 / 2

so either , x = 6/2 = 3

or x = 10/2 = 5

Hope it helps.