If p(x)=3 x^2+9 x+7 and p(a)=2, then a= (A) only 0.736 (B) only 0.736 (C) 0.736 or 2.264 (D) 0.7

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If p(x)=3 x^2+9 x+7 and p(a)=2, then a= (A) only 0.736 (B)...

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Key Concepts

Quadratic Polynomial

A quadratic polynomial is an expression of the form ax² + bx + c, where a, b, and c are constants and a ? 0. These polynomials represent parabolic curves in a coordinate plane and form the basis for studying quadratic equations and their properties.

Solving Quadratic Equations

Solving quadratic equations involves finding the values of x that satisfy an equation of the form ax² + bx + c = 0. This can be accomplished by methods such as factoring, completing the square, or applying the quadratic formula, each method providing a systematic approach to determine the roots.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac))/(2a), is a universal solution technique for quadratic equations. It directly computes the roots of any quadratic equation based on its coefficients, making it a valuable tool in algebra that handles both real and complex solutions.

Discriminant

The discriminant, found under the square root in the quadratic formula as b² - 4ac, reveals the nature of the quadratic equation's roots. A positive discriminant indicates two distinct real roots, zero signifies a single repeated real root, and a negative discriminant indicates a pair of complex conjugate roots.

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