Question

8 times of a number is added to its square give a result -15. Then find the number by us
quadratic equation​

Answer 1

Answer:

Let the Required Number be n.

☯ According to the Question :

⇢ 8(Number) + (Number)² = – 15

⇢ 8n + n² = – 15

⇢ n² + 8n + 15 = 0

⇢ n² + (5 + 3)n + 15 = 0

⇢ n² + 5n + 3n + 15 = 0

⇢ n(n + 5) + 3(n + 5) = 0

⇢ (n + 3)(n + 5) = 0

⇢ n = – 3⠀or,⠀n = – 5

∴ Hence, Number can be either – 3 or – 5.

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☢ VERIFICATION :

⋆ When Number = – 3

⟶ 8n + n² = – 15

⟶ 8(– 3) + (– 3)² = – 15

⟶ – 24 + 9 = – 15

⟶ – 15 = – 15 ⠀⠀Hence, Verified!

⋆ When Number = – 5

⟶ 8n + n² = – 15

⟶ 8(– 5) + (– 5)² = – 15

⟶ – 40 + 25 = – 15

⟶ – 15 = – 15 ⠀⠀Hence, Verified!

Answer 2

AnswEr :

Let the Number be x.

☯⠀$\underline{\textsf{Let's Head to the Question Now :}}$

$:\implies\sf 8\:Times\:of\:Number+(Number)^2=-15\\\\\\:\implies\sf 8x + x^2 = - 15\\\\\\:\implies\sf x^2 + 8x + 15 = 0\\\\\\:\implies\sf x^2 + 5x + 3x + 15 = 0\\\\\\:\implies\sf x(x + 5) + 3(x + 5) = 0\\\\\\:\implies\sf (x + 5)(x + 3) = 0\\\\\\:\implies \boxed{\red{\sf x = -\:5}\quad \sf or \quad \red{x = -\:3}}$