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Gr 11 Math Ch 2: Finding the Equation

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Questions and Answers

What is the first step in finding the quadratic equation given the roots?

Expand the brackets to get the quadratic equation

Assign a variable and write roots as two equations (correct)

Multiply the binomials to get the quadratic equation

Write the quadratic equation in the standard form

What is the purpose of using additive inverses in finding the quadratic equation?

To get rid of the roots

To multiply the binomials

To expand the brackets

To get zero on the right-hand sides of the equations (correct)

What is the form of the quadratic equation obtained after writing down as the product of two factors?

x^2 + bx + c = 0

(x - r_1)(x - r_2) = 0 (correct)

x^2 - bx + c = 0

ax^2 + bx + c = 0

What is the purpose of multiplying by constants in finding the quadratic equation?

To get other possible equations with the same roots Signup and view all the answers

What is the final form of the quadratic equation obtained after expanding the brackets?

ax^2 + bx + c = 0 Signup and view all the answers

What is the result of writing the roots as two equations in the process of finding a quadratic equation?

x - r₁ = 0 and x - r₂ = 0 Signup and view all the answers

What is the purpose of expanding the brackets in the process of finding a quadratic equation?

To get the quadratic equation in standard form Signup and view all the answers

If the roots of a quadratic equation are 2 and 3, what is the quadratic equation in factorized form?

(x - 2)(x - 3) = 0 Signup and view all the answers

What is the effect of multiplying each term in the quadratic equation by a constant?

The equation remains the same Signup and view all the answers

What is the quadratic equation if the roots are -1 and -4?

x² + 5x + 4 = 0 Signup and view all the answers

If the roots of a quadratic equation are 5 and -3, what is the product of the x-coefficients in the standard form?

-23 Signup and view all the answers

What is the primary reason for writing the roots as two equations in the process of finding a quadratic equation?

To obtain the additive inverses Signup and view all the answers

Given the quadratic equation (x - 2)(x + 4) = 0, what would be the result of multiplying each term in the equation by -2?

The coefficient of the x^2 term would become -2 Signup and view all the answers

What is the significance of the zero on the right-hand side in the equations x - r1 = 0 and x - r2 = 0?

It enables us to use the additive inverses Signup and view all the answers

What is the relationship between the quadratic equation (x - r1)(x - r2) = 0 and the standard form ax^2 + bx + c = 0?

The first is the factorized form, and the second is the expanded form Signup and view all the answers