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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

10. Roots and Zeros

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Exercise 20 Page 77

Make sure you write all the terms on the left-hand side of the equation and simplify as much as possible before using the Quadratic Formula.

Roots: x= 5± isqrt(87)4
Number and Type of Roots: two imaginary roots

Practice makes perfect

We will use the Quadratic Formula to solve the given quadratic equation. ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 aWe first need to identify the values of a, b, and c. 2x^2-5x+14=0 ⇕ 2x^2+( - 5)x+ 14=0 We see that a= 2, b= - 5, and c= 14. Let's substitute these values into the Quadratic Formula. Remember that sqrt(- a)= isqrt(a).

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -5)±sqrt(( - 5)^2-4( 2)( 14))/2( 2)

▼

Evaluate right-hand side

- (- a)=a

x=5±sqrt((- 5)^2-4(2)(14))/2(2)

Calculate power

x=5±sqrt(25-4(2)(14))/2(2)

Multiply

x=5±sqrt(25-112)/4

Add terms

x=5±sqrt(- 87)/4

sqrt(- a)= isqrt(a)

x = 5 ± isqrt(87)/4

Using the Quadratic Formula, we found that the roots of the given equation are x= 5± isqrt(87)4. Both of them are imaginary.

Subchapter links

Exercises p.77-79