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If an Integer is Added to Its Square, the Sum is 90. Find the Integer with the Help of Quadratic Equation. - CBSE Class 10 - Mathematics

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Question

If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

Solution

Let the integer be ‘x’

Given that if an integer is added to its square, the sum is 90.

⇒ 𝑥 + 𝑥2 = 90

⇒ 𝑥 + 𝑥2 − 90 = 0

⇒ 𝑥2 + 10𝑥 - 9𝑥 - 90 = 0

⇒ 𝑥(𝑥 + 10) - 9(𝑥 + 10) = 0

⇒ x = -10 or x = 9

∴ The value of an integer are -10 or 9.

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Solution If an Integer is Added to Its Square, the Sum is 90. Find the Integer with the Help of Quadratic Equation. Concept: Solutions of Quadratic Equations by Factorization.
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