A quadratic equation has roots 3 and 7. Write the equation and compute its discriminant.

medium 3 marks Class 8 · Mathematics · Algebraic Expressions and Identities

Answer

Equation:

x^{2} - 10 x + 21 = 0

. Discriminant:

16

The correct answer is Equation: $x^{2} - 10 x + 21 = 0$ . Discriminant: $16$ — Therefore the discriminant is $16$ .

Step-by-step solution

Sum of roots: $3 + 7 = 10$ ; product: $3 \times 7 = 21$ .
Write the quadratic in standard form: $x^{2} - (sum) x + (product) = 0$ , giving $x^{2} - 10 x + 21 = 0$ .
Compute the discriminant: $D = b^{2} - 4 a c = (- 10)^{2} - 4 (1) (21) = 100 - 84 = 16$ .
Therefore the discriminant is $16$ .

Common mistake: Using

b

as the sum instead of

-

sum or miscalculating the product

Concept tested: Root–coefficient relationships