What is the value of 'a' in the equation 2x2 + (10 - a)x + 25 = 0 if

1.	What is the value of 'a' in the equation 2x2 + (10 - a)x + 25 = 0 if 'a' is one of the factor of the equation. Also find the other factor.1. a = -2.5, b = -52. a = -5, b = -2.53. a = 5, b = 2.54. a = 2.5, b = 5
Answer» Correct Answer - Option 2 : a = -5, b = -2.5 Concept: For an equation ax2 + bx +c = 0 Sum of the roots = \(\rm-b\over a\) Product of the roots = \(\rm c\over a\) Roots of the equation = \(\rm x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) If α and β are the roots of the equation the equation can be represented as (x - α)(x - β) = 0 The roots of a quadratic equation ax2 +bx + c = 0 are real if: b2 - 4ac ≥ 0 Calculation: 2x2 + (10 - a)x + 25 = 0 ∵ a is the factor of the equation ⇒ 2a² + (10 - a)a + 25 = 0 ⇒ a² + 10a + 25 = 0 ⇒ (a + 5)² = 0 ⇒ a = - 5 Putting a in the equation 2x² + (10 - (-5)) x + 25 = 0 2x² + 15x + 25 = 0 (x + 5)(2x + 5) = 0 x = -5, -2.5

What is the value of 'a' in the equation 2x2 + (10 - a)x + 25 = 0 if 'a' is one of the factor of the equation. Also find the other factor.1. a = -2.5, b = -52. a = -5, b = -2.53. a = 5, b = 2.54. a = 2.5, b = 5

Answer» Correct Answer - Option 2 : a = -5, b = -2.5

Concept:

For an equation ax2 + bx +c = 0

Sum of the roots = \(\rm-b\over a\)
Product of the roots = \(\rm c\over a\)
Roots of the equation = \(\rm x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
If α and β are the roots of the equation the equation can be represented as (x - α)(x - β) = 0

The roots of a quadratic equation ax2 +bx + c = 0 are real if:

b2 - 4ac ≥ 0

Calculation:

2x2 + (10 - a)x + 25 = 0

∵ a is the factor of the equation

⇒ 2a² + (10 - a)a + 25 = 0

⇒ a² + 10a + 25 = 0

⇒ (a + 5)² = 0

⇒ a = - 5

Putting a in the equation

2x² + (10 - (-5)) x + 25 = 0

2x² + 15x + 25 = 0

(x + 5)(2x + 5) = 0

x = -5, -2.5

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What is the value of 'a' in the equation 2x2 + (10 - a)x + 25 = 0 if 'a' is one of the factor of the equation. Also find the other factor.1. a = -2.5, b = -52. a = -5, b = -2.53. a = 5, b = 2.54. a = 2.5, b = 5

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