Solve using the quadratic formula.4y2+7y−2=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.y=_____ or y=_____
Q. Solve using the quadratic formula.4y2+7y−2=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.y=_____ or y=_____
Identify coefficients: Identify the coefficients a, b, and c in the quadratic equation4y2+7y−2=0 by comparing it to the standard form ax2+bx+c=0.a=4, b=7, c=−2
Write quadratic formula: Write down the quadratic formula, which is y=2a−b±b2−4ac.
Substitute values: Substitute the values of a, b, and c into the quadratic formula.y=2(4)−(−7)±(7)2−4(4)(−2)
Simplify discriminant: Simplify the expression under the square root (the discriminant). (7)2−4(4)(−2)=49+32=81
Calculate square root: Calculate the square root of the discriminant. 81=9
Insert square root: Insert the value of the square root back into the quadratic formula.y = (−7±9)/8
Calculate solutions: Calculate the two possible solutions for y.y=8−7+9 or y=8−7−9y=82 or y=8−16
Simplify fractions: Simplify the fractions to get the solutions in simplest form. y=41 or y=−2
Round non-integer: If necessary, round the non-integer solution to the nearest hundredth.Since 41 is already in simplest form and is a proper fraction, no rounding is needed.
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