Which of the following quadratic equations can be solved by grouping?(1 point)
Responses
x2−12x+18=0
x squared minus 12 x plus 18 equals 0
x2+10x+21=0
x squared plus 10 x plus 21 equals 0
x2−4x−8=0
x squared minus 4 x minus 8 equals 0
x2+8x−22=0
x squared plus 8 x minus 22 equals 0
The quadratic equation that can be solved by grouping is:
x2−4x−8=0
(x-2)(x-4)=0
a b c or d
C) x2−4x−8=0
To determine which of the given quadratic equations can be solved by grouping, we need to check if the coefficient of the middle term (the x-term) is twice the square root of the product of the coefficients of the first and last terms.
Let's go through each equation and find the coefficient of the middle term:
1) x^2 - 12x + 18 = 0
The coefficient of the middle term is -12.
2) x^2 + 10x + 21 = 0
The coefficient of the middle term is 10.
3) x^2 - 4x - 8 = 0
The coefficient of the middle term is -4.
4) x^2 + 8x - 22 = 0
The coefficient of the middle term is 8.
Now, let's calculate the square root of the product of the coefficients of the first and last terms:
1) sqrt(1 * 18) = sqrt(18)
2) sqrt(1 * 21) = sqrt(21)
3) sqrt(1 * -8) = sqrt(-8) (Negative value, so we know grouping won't work)
4) sqrt(1 * -22) = sqrt(-22) (Negative value, so we know grouping won't work)
From the calculations, we see that only equations 1) and 2) have coefficients of the middle term that are twice the square root of the product of the coefficients of the first and last terms. Therefore, the quadratic equations that can be solved by grouping are:
1) x^2 - 12x + 18 = 0
2) x^2 + 10x + 21 = 0