I. Use the quadratic formula to solve each of the following quadratic equations:
a. x² - 9x = -10
b. 2m² + 13m + 20 = 0
c. 2y² + 8y = 9
d. 9t-5t² = -12
e. 3b² + 13b + 20 = 0
II. Solve for the unknown in the problem using the quadratic formula. The area of a table cloth is 7 square ft. If the wifth is 3 feet shorter than the length, then what are the dimensions of the table cloth?
Answer:
Answer【Answer】:
1.I.a. x = 1, 10
1.I.b. m = -4, -5/2
1.I.c. y = -1, 9/2
1.I.d. t = -1.6, 6
1.I.e. b = -4, -5/2
2.II. l = 3, w = 0
【Explanation】:
I.a. By rearranging the equation x^2-9x = -10, we get x^2-9x+10 = 0. When applying the quadratic formula to solve it, we use a= 1, b= -9 and c= 10 to get x = 1, 10.
I.b. For the equation 2m^2+13m+20=0, a=2 , b=13, and c=20 in the quadratic formula, and upon calculation we get m =-4, -5/2.
I.c. The equation 2y^2+8y= 9 can be rearranged to 2y^2+8y -9= 0. Upon Applying the quadratic formula where a=2, b=8, and c=-9, we get y=-1 and 9/2.
I.d. Rewriting the equation 9t-5t^2=-12 as -5t^2 + 9t +12 we get a=-5, b= 9, and c= 12. These are substituted into the formula and we get t = -1.6, 6.
I.e. In the equation 3b^2+13b+20 = 0, coefficients are a=3, b=13 and c=20 which when substituted in the quadratic formula, we get b = -4, -5/2.
II. By setting up a quadratic equation length*width = 7, water and claiming that width is 3 feet shorter than the length it gives the formula l^2 - 3l -7 =0. When applying the quadratic formula with coefficients a=1, b=-3 and c=-7 gives that l=3.