Free Printable Solving quadratic equation with no constant

1.

The zero product property tells us that if the product of any number of expressions is zero, at least one of them must be zero.

Which of the following equations may be solved using that property? Check ALL that applies.

a)

$2\cdot x\cdot y=0$

b)

$\left(x-1\right)\cdot\left(x-4\right)=0$

c)

$2\cdot a\cdot b=18$

d)

$\left(p+3\right)\cdot p=1000$

e)

$x\cdot\left(3x-1\right)=0$

2.

Whaich of the following equations are quadratic equations with no constant?

Check ALL that applies.

a)

$x^2-4x=0$

b)

$5x^2+x=0$

c)

$-m^2-1000m=0$

d)

$-0.4p^2+4=0$

e)

$81k^2-\frac{1}{4}k=0$

3.

Which of the following equations can be written as a quadratic equation with no constant (in the form $ax^2+bx=0$ ) ? Check ALL that applies.

a)

$2x^2=-5x$

b)

$-3x^2+6x=9$

c)

$1000x=10x^2$

d)

$−𝑥^2−3𝑥=−4𝑥^2$

e)

$(2+𝑥)𝑥=3𝑥^2+4𝑥$

4.

Solve the following equation:
$x\left(x+1\right)=0$

a)

$x=0$

b)

$x=0\ ,\ x=-1$

c)

$x=0\ ,\ x=1$

d)

$x=-\frac{1}{2}$

5.

Solve the equation:
$𝑥^2+11𝑥=0$

a)

$x=0,\ x=-11$

b)

$x=0,\ x=11$

c)

$x=-11$

d)

$x=\pm\sqrt{-11x}$

6.

How can you factor equation
$-4x^2+9x=0$ ?
Check ALL expressions equivalent with the equation.

a)

$x\left(-4x+9\right)=0$

b)

$-x^2\left(4-9x\right)=0$

c)

$-x\left(4x-9\right)=0$

d)

$-x\left(4x+9\right)=0$

7.

Solve $p^2+4p=0$

a)

$p=0,\ p=4$

b)

$p=0,\ p=-4$

c)

$p=0$

d)

$p=\pm2$

8.

Solve $−𝑥^2+25𝑥=−6𝑥^2$

a)

$x=0,\ x=-5$

b)

$x=0,\ x=5$

c)

$x=-5,\ x=5$

d)

no solution

9.

Solve $3𝑥^2+4x=(2+𝑥)𝑥$

a)

$x=0,\ x=-1$

b)

$x=0,\ x=1$

c)

$x=0,\ x=-2$

d)

$x=0,\ x=2$

10.

Solve $12a^2=108a$ .

Write solution(s) (numbers) below. If there is more than one solution, separate numbers with a comma and no space (example: -2,321)

(a)

Solving quadratic equation with no constant

Total questions: 10

Worksheet time: 3600secs

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