Question

match the following quadratics to their zeros.
$x^2 + 10x + 21 = 0$
$x^2 + 76x + 75 = 0$
$x^2 + 32x + 31 = 0$
$x^2 - 22x + 40 = 0$
$x^2 - 18x - 19 = 0$
$x^2 + 6x - 27 = 0$
$x = -3, x = -7$
$x = -1, x = -31$
$x = -9, x = 3$
$x = -1, x = -75$
$x = 2, x = 20$
$x = -1, x = 19$

Explanation:

Step1: Factor \(x^2 + 10x + 21 = 0\)

Find two numbers that multiply to \(21\) and add to \(10\). The numbers are \(3\) and \(7\). So, \((x + 3)(x + 7)=0\). Setting each factor to zero gives \(x=-3\) or \(x=-7\).

Step2: Factor \(x^2 + 76x + 75 = 0\)

Find two numbers that multiply to \(75\) and add to \(76\). The numbers are \(1\) and \(75\). So, \((x + 1)(x + 75)=0\). Setting each factor to zero gives \(x=-1\) or \(x=-75\).

Step3: Factor \(x^2 + 32x + 31 = 0\)

Find two numbers that multiply to \(31\) and add to \(32\). The numbers are \(1\) and \(31\). So, \((x + 1)(x + 31)=0\). Setting each factor to zero gives \(x=-1\) or \(x=-31\).

Step4: Factor \(x^2 - 22x + 40 = 0\)

Find two numbers that multiply to \(40\) and add to \(-22\). The numbers are \(-2\) and \(-20\). So, \((x - 2)(x - 20)=0\). Setting each factor to zero gives \(x=2\) or \(x=20\).

Step5: Factor \(x^2 - 18x - 19 = 0\)

Find two numbers that multiply to \(-19\) and add to \(-18\). The numbers are \(-19\) and \(1\). So, \((x - 19)(x + 1)=0\). Setting each factor to zero gives \(x=19\) or \(x=-1\).

Step6: Factor \(x^2 + 6x - 27 = 0\)

Find two numbers that multiply to \(-27\) and add to \(6\). The numbers are \(9\) and \(-3\). So, \((x + 9)(x - 3)=0\). Setting each factor to zero gives \(x=-9\) or \(x=3\).

Answer:

• \(x^2 + 10x + 21 = 0\) matches \(x = -3, x = -7\)
• \(x^2 + 76x + 75 = 0\) matches \(x = -1, x = -75\)
• \(x^2 + 32x + 31 = 0\) matches \(x = -1, x = -31\)
• \(x^2 - 22x + 40 = 0\) matches \(x = 2, x = 20\)
• \(x^2 - 18x - 19 = 0\) matches \(x = -1, x = 19\)
• \(x^2 + 6x - 27 = 0\) matches \(x = -9, x = 3\)