The quadratic formula finds solutions (x-values) where ax² + bx + c = 0. For any quadratic equation the roots are x = [-b ± √(b² – 4ac)] / (2a) where b² – 4ac is called the discriminant and determines whether the equation has real or imaginary roots.
A quadratic equation takes the form ax² + bx + c = 0 where a b and c are real numbers and a ≠ 0. The quadratic formula x = [-b ± √(b² – 4ac)] / (2a) helps find the roots of any quadratic equation. The discriminant b² – 4ac determines the nature of roots which can be real and equal real and unequal or imaginary based on its value.For your CBSE board exam focus on solving equations using factorization completing the square and the quadratic formula. Practice finding roots and understanding their nature and relationships based on the discriminant.
For quadratic equation x² – 5x + 6 = 0
Let’s solve using factorization method:
x² – 5x + 6 = 0
x² – 2x – 3x + 6 = 0
x(x – 2) – 3(x – 2) = 0
(x – 2)(x – 3) = 0
Therefore x = 2 or x = 3
The roots of the equation are 2 and 3.
Hence option “2, 3” is correct.
We can verify:
When x = 2: 2² – 5(2) + 6 = 4 – 10 + 6 = 0
When x = 3: 3² – 5(3) + 6 = 9 – 15 + 6 = 0
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