Let me explain how to find these values without equations. When we have a quadratic expression with two roots the sum appears as the negative of the coefficient of x term divided by the coefficient of x² term. The product appears as the constant term divided by the coefficient of x² term. For example if we have roots -2 and 5 then their sum would be 3 and their product would be -10.
A quadratic equation is a polynomial equation of degree 2 which can be written in the standard form ax² + bx + c = 0 where a and b and c are real numbers and a ≠ 0. This topic builds on your understanding of polynomials from Class 9 and introduces methods to find solutions or roots of these equations. The chapter covers important concepts like factorization split middle term method completing the square method and quadratic formula. You’ll also learn about the nature of roots the relationship between discriminant and roots and applications of quadratic equations in real-world problems. This understanding serves as a foundation for higher mathematical concepts in Class 11 and 12 especially in topics like calculus and coordinate geometry.
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Given quadratic equation: 2x² – 7x + 3 = 0
For a quadratic equation ax² + bx + c = 0:
Sum of roots = -b/a
Product of roots = c/a
Here:
a = 2
b = -7
c = 3
Sum of roots = -(-7)/2 = 7/2
Product of roots = 3/2
To verify:
– If we solve for roots using quadratic formula, and add them, we get 7/2
– If we multiply those roots, we get 3/2
Hence, 7/2, 3/2 is the correct answer for sum and product of roots respectively.
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