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Find the zeros of the function f(x)=1.4x^(2)+6.9 x+3. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=1.4x2+6.9x+3 f(x)=1.4 x^{2}+6.9 x+3 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=1.4x2+6.9x+3 f(x)=1.4 x^{2}+6.9 x+3 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Write Quadratic Equation: Write down the quadratic equation.\newlineThe given function is f(x)=1.4x2+6.9x+3f(x) = 1.4x^2 + 6.9x + 3. To find the zeros of the function, we need to solve for xx when f(x)=0f(x) = 0.
  2. Apply Quadratic Formula: Apply the quadratic formula to find the zeros.\newlineThe quadratic formula 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. In this case, a=1.4a = 1.4, b=6.9b = 6.9, and c=3c = 3.
  3. Calculate Discriminant: Calculate the discriminant b2−4acb^2 - 4ac.\newlineDiscriminant, D=b2−4ac=(6.9)2−4(1.4)(3)=47.61−16.8=30.81D = b^2 - 4ac = (6.9)^2 - 4(1.4)(3) = 47.61 - 16.8 = 30.81.
  4. Calculate Values for x: Calculate the two possible values for x using the quadratic formula.\newlinex=−6.9±30.812×1.4x = \frac{-6.9 \pm \sqrt{30.81}}{2 \times 1.4}\newlineFirst, we find the square root of the discriminant: 30.81≈5.55\sqrt{30.81} \approx 5.55.
  5. Solve for First Zero: Solve for the first zero (using the '+' in '±\pm').\newlinex1=−6.9+5.552×1.4=−1.352.8≈−0.48x_1 = \frac{-6.9 + 5.55}{2 \times 1.4} = \frac{-1.35}{2.8} \approx -0.48.
  6. Solve for Second Zero: Solve for the second zero (using the '-' in '±\pm').\newlinex2=(−6.9−5.55)(2×1.4)=(−12.45)(2.8)≈−4.45.x_2 = \frac{(-6.9 - 5.55)}{(2 \times 1.4)} = \frac{(-12.45)}{(2.8)} \approx -4.45.

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