SAT Math Question for the week of 08/29/2021

What is the sum of the roots of the equation 2x^2 - 7x + 3 ?

Maps to Category 27 of the book.

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Answer posted on 09/05/2021: Answer is 3.5 or 7/2.

The two factors are (2x-1) = 0 and (x-3) = 0.

Hence, the two roots are 1/2 or 0.5 and 3.

The sum of the roots is 1/2 + 3 = 3.5 or 7/2

SAT Math Question for the week of 08/22/2021

The equation ax + b = -5x + b has infinitely many solutions, where a and b are constants. What is the value of a?

Maps to Category 10 of the book.

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Answer posted on 08/29/2021: Answer is -5.

For an equation to have infinitely many solutions, expressions on both side of the equation must be equal. Since the value of constant b is same on both sides, a must be -5.

SAT Math Question for the week of 08/15/2021

What is the x-intercept of a line passing through the points (-1, 1.5) and (0, 4)?

Maps to Category 1 of the book.

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Answer posted on 08/22/2021: Answer is -1.6 or -4/2.5.

Since x = 0 at y-intercept, the given point (0, 4) is the y-intercept of the line.

Determine the slope, and plug the slope and the y-intercept in the y = mx + b equation.

Slope = (4 - 1.5)/(0-(-1)) = 2.5/1 = 2.5.

Hence, the equation is y = 2.5x + 4.

Since y = 0 at x-intercept, set y = 0 in the above equation and solve for x.

0 = 2.5x + 4 --> 2.5x = -4 --> x = -4/2.5 = -1.6.