Question

quadratic functions and equations
finding the roots of a quadratic equation with leading coefficient 1
solve for v.
$v^2 + 3v - 28 = 0$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
$v = \square$

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to -28 and add up to 3. The numbers are 7 and -4, since \(7\times(-4)= -28\) and \(7 + (-4)=3\). So we can factor the quadratic as \((v + 7)(v - 4)=0\).

Step2: Solve for v

Set each factor equal to zero:

• For \(v + 7 = 0\), subtract 7 from both sides: \(v=-7\).
• For \(v - 4 = 0\), add 4 to both sides: \(v = 4\).

Answer:

-7, 4