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Q.17. Find the value of a and b for the following algebraic expressions.
(a) $m^{2} - a m + 10 = (m - b) (m - 5)$
(b) $a z^{2} + 10 z - 75 = (z + b) (5 z - 15)$

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Solution

Dear student
$(a) m^{2} - a m + 10 = (m - b) (m - 5) C o n s i d e r, R H S (m - b) (m - 5) = m^{2} - 5 m - b m + 5 b = m^{2} - (5 + b) m + 5 b O n c o m p a r i n g w i t h L H S, w e g e t a = 5 + b a n d 5 b = 10 \Rightarrow a = 5 + 2 b = 2 \Rightarrow a = 7 a n d b = 2 (b) a z^{2} + 10 z - 75 = (z + b) (5 z - 15) C o n s i d e r, R H S (z + b) (5 z - 15) = 5 z^{2} - 15 z + 5 b z - 15 b = 5 z^{2} + (5 b - 15) z - 15 b O n c o m p a r i n g w i t h L H S, w e g e t a = 5 a n d - 15 b = - 75 \Rightarrow b = 5$
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a z^{2} + 10 z - 75 = (z + b) (5 z - 15)

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