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f(x) be a quadratic polynomial f(x) = (...

f(x) be a quadratic polynomial ` f(x) = (x-1) (ax+b)` satisfying `f(2) + f(4) = 0.`
If unity is one root of f(x) = 0 then find the other root.

Text Solution

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From the given information,
` f(x) = (x-1) (ax+b)`
So, `" " f(2) = 2a + b`
and " " `f(4) = 3(4a + b) = 12a + 3b`
Given that `f(2) + f(4) = 0`
`rArr " " 14a + 4b = 0`
`rArr " " b = - (7a)/(2)`
`therefore" " Equation is (x-1)(ax-(7a)/(2))=0`
Therefore, other root is `7//2`
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