Question

if 1 is the root of
$a {x}^{2} + 3x + 5 = 0$
find the second root...

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Answer 1

Solution :-

Given that, 1 is the root of ax² + 3x + 5 = 0

Than, Putting x = 1, we get, remainder = 0

→ f(x) = ax² + 3x + 5

→ f(1) = a(1)² + 3*1 + 5

→ f(1) = a + 8

→ a + 8 = 0

→ a = (-8)

Now, The Equation is :- (-8)x²+ 3x + 5 = 0

or,

→ 8x² - 3x - 5 = 0

→ 8x² - 8x + 5x - 5 = 0

→ 8x(x - 1) + 5(x - 1) = 0

→ (8x + 5)(x - 1) = 0

→ (8x + 5) = 0

→ x = (-5/8)

or,

→ (x - 1) = 0

→ x = 1 .

Hence, second root of given equation is (-5/8).