Q9 of 157 Page 22

If (x + a) (x + b) = x2 – 5x – 300, find the values of a2 + b2.

Given: (x + a) (x + b) = x2 – 5x – 300


Using (x + a)(x + b) = x2 + (a + b)x + ab


⇒ x2 + (a + b)x + ab = x2 – 5x – 300


⇒ (a + b) = – 5 and ab = – 300


Also, a2 + b2 = (a+ b)2 – 2ab


⇒ a2 + b2 = ( – 5)2 – 2( – 300)


⇒ a2 + b2 = 25 + 600


⇒ a2 + b2 = 625


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