Prove-style reasoning: For the quadratic equation x^2 - 2(a+b)x + (a^2 + b^2 + c) = 0 to have equal roots, the discriminant gives a relation. Simplify D = 0 to find what c must equal.

Question

Accepted Answer

c = 2ab. D = 0: [2(a+b)]^2 - 4(a^2+b^2+c) = 0 => 4(a+b)^2 = 4(a^2+b^2+c) => (a+b)^2 = a^2+b^2+c => a^2+2ab+b^2 = a^2+b^2+c => c = 2ab.

Prove-style reasoning: For the quadratic equation $x^{2} - 2 (a + b) x + (a^{2} + b^{2} + c) = 0$ to have equal roots, the discriminant gives a relation.
Simplify $D = 0$ to find what $c$ must equal.

Step-by-Step Solution

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More Class 10 Nature of Roots (Discriminant) practice

Prove-style reasoning: For the quadratic equation x2−2(a+b)x+(a2+b2+c)=0 to have equal roots, the discriminant gives a relation.Simplify D=0 to find what c must equal.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Nature of Roots (Discriminant) practice

Prove-style reasoning: For the quadratic equation $x^{2} - 2 (a + b) x + (a^{2} + b^{2} + c) = 0$ to have equal roots, the discriminant gives a relation.
Simplify $D = 0$ to find what $c$ must equal.