Question

Find the values of m for which the equation (m +1) x² + 2 (m +2)x+ m = 0

have equal roots
a. - 0.5
b. -4/3
c. 1
d. None of the above
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Answer 1

★Given :

• The equation  (m +1) x² + 2 (m +2)x+ m = 0 has equal roots.

★To find :

• Value of m.

★Solution :

Concept ::

A quadratic equation ax²+bx+c=0 where a,b,c are real numbers and a≠0 has equal roots if its discriminant b²-4ac is zero.That is,

• b²- 4ac=0

Given equation :

• (m +1) x² + 2 (m +2)x+ m = 0  

Finding the discriminant :

→b²- 4ac

→[2(m+2)]² - 4(m+1)(m)

→4(m²+4m+4) - 4m² - 4m

→4m² + 16m + 16 - 4m² - 4m

→12m + 16

For equal roots,discriminant is zero.Therefore,

→12m + 16  = 0

→12m = -16

→m = -16/12

→m = -4/3

∴Option(B) is correct.

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