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Find the zeros of the function f(x)=2x^(2)-19 x+42. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=2x2−19x+42 f(x)=2 x^{2}-19 x+42 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=2x2−19x+42 f(x)=2 x^{2}-19 x+42 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Use Quadratic Formula: To find the zeros of the function f(x)=2x2−19x+42f(x) = 2x^2 - 19x + 42, we need to solve the quadratic equation 2x2−19x+42=02x^2 - 19x + 42 = 0. We can use the quadratic formula, which is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0.
  2. Identify Coefficients: In our equation, a=2a = 2, b=−19b = -19, and c=42c = 42. Plugging these values into the quadratic formula, we get:\newlinex=−(−19)±(−19)2−4⋅2⋅422⋅2x = \frac{-(-19) \pm \sqrt{(-19)^2 - 4 \cdot 2 \cdot 42}}{2 \cdot 2}\newlinex=19±361−3364x = \frac{19 \pm \sqrt{361 - 336}}{4}\newlinex=19±254x = \frac{19 \pm \sqrt{25}}{4}
  3. Apply Quadratic Formula: Simplify the square root and the expression:\newlinex=19±54x = \frac{19 \pm 5}{4}\newlineThis gives us two solutions:\newlinex=(19+5)4x = \frac{(19 + 5)}{4} and x=(19−5)4x = \frac{(19 - 5)}{4}\newlinex=244x = \frac{24}{4} and x=144x = \frac{14}{4}
  4. Simplify Expression: Divide to find the zeros:\newlinex=244=6x = \frac{24}{4} = 6 and x=144=3.5x = \frac{14}{4} = 3.5

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