Question

Write a quadratic equation in standard form with ="\frac{3}{4}" alt="\frac{3}{4}" align="absmiddle" class="latex-formula"> an -5 as its roots

Answer 1

STANDARD FORM:

• ax² + bx + c

ANSWER:

If {a,b} are roots of a quadratic equation (say with variable x) f(x) = 0, then f(a) and f(b) are both equal to zero. It means that the equation is of type (x − a)(x − b) = 0

Hence, the quadratic equation with roots 3/4 and - 5 as its roots are:

• (x – 3/4)(x + 5)
• x(x + 5) – 3/4(x + 5)
• x² + 5x – 3/4x – 15/4
• x² + (20x – 3x/4) – 15/4
• x² + 17x/4 – 15/4
• 1/4(4x² + 17x – 15)

Answer 2

Knowing the roots first write the equation in factored form:

(X - 3/4)(x +5) = 0

Now use the FOIL method ( multiply each term in one set of parentheses by each term the other set:

X•x + x•5 -3/4•x -3/4•5

Simplify:

X^2 + 5x -3/4x -3 3/4

Combine like terms:

X^2+ 4 1/4x - 3 3/4