Which of the following equations have real & equal roots
(1) $4 x^{2} + 20 x + 25 = 0$
(2) $6 x^{2} - 9 x - 4 = 0$
(3) $4 x^{2} + 9 x + 5 = 0$

only 1

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only 1 & 2

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only 2 & 3

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All of the above

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Solution

The correct option is A
only 1

(1) $4 x^{2} + 20 x + 25; D = (20)^{2} - 4 \times 4 \times 25$ = 400 - 400 = 0
-Real & equal roots
(2) $6 x^{2} - 9 x - 4; d = - (9)^{2} - 4 \times 6 \times - 4$ = 36 - 96 < 0
-No real roots
(3) $4 x^{2} + 9 x + 5 = 0; D = (9)^{2} - 4 \times 4 \times 5$ = 81 - 80 > 0
Two distinct real roots

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4 x^{2} + 20 x + 25

What must be subtracted from $(x^{3} - 3 x^{2} + 5 x - 1)$ to get $(2 x^{3} + x^{2} - 4 x + 2)$ ?

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