An equation shows that two mathematical expressions have the same value using an equals sign (=). It can involve numbers variables functions and mathematical operations to express relationships. Equations help us solve problems find unknown values and describe mathematical patterns in algebra and other fields.
A quadratic equation is a polynomial equation of degree two expressed in the form ax² + bx + c = 0 where a b and c are real numbers and a ≠ 0. The solutions or roots of a quadratic equation can be found using various methods including factorization completing the square and quadratic formula. Real-world applications involve areas volumes time distance relationships projectile motion and business profit calculations. Students should master these concepts thoroughly for the CBSE Class 10 Board Examination of 2024-25.
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Given equation: x² + px + 12 = 0
One root is -3
Since -3 is a root it must satisfy the equation:
(-3)² + p(-3) + 12 = 0
Simplifying:
9 – 3p + 12 = 0
21 – 3p = 0
-3p = -21
p = 7
To verify:
When p = 7:
x² + 7x + 12 = 0
Roots are -3 and -4
One root is indeed -3
Hence, 7 is the correct answer.
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