Question

if one zero of the polynomial X square + bx + c is double The Other prove that 2 b square is equal to 9 a c​

Answer 1

CORRECT QUESTION:

If one zero of the polynomial ax² + bx + c is double the other . Then prove that 2b² = 9ac

ANSWER:

Given polynomial

x² + bx + c

Let α , β be the roots of the given polynomial

ax² + bx + c

★ We know that :

Sum of roots = -b/a

Product of roots = c/a

♦ Given condition:

• One root is double the other
• α = 2β

Roots are α , 2α

.°. α + 2α = - b/a

α.2α = c/a

→ 3α = - b/a

α = - b/3a

Assuming as equation (1)

→ 2α² = c/a

α² = c/2a

(-b/3a)² = c/2a. [ Using equation (1)]

b²/9a² = c/2a

b²/9a = c/2

2b² = 9ac

Hence, proved

Answer 2

Answer:

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