Advertisements
Advertisements
Question
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
Advertisements
Solution
The given quadratic equation is
`(x - 1)^2 - 3x + 4 = 0`
`=> x^2 - 2x + 1 - 3x + 4 = 0`
`=> x^2 - 5x + 5 = 0`
The roots of the quadratic equation ax2 + bx + c = 0 are given by
`x = (-b+- sqrt(b^2 - 4ac))/"2a"`
In the given equation,
a = 1, b = –5, c = 5
Thus, the roots of the equation are
`x= (-(-5)+- sqrt((-5)^2 -4(1(5))))/(2(1))`
`=> X = (5 +- sqrt(25 - 20))/2`
`=> x = (5+ sqrt5)/2`
`=> x = (5 + sqrt5)/2 or x = (5-sqrt5)/2`
⇒ x = 3.618 or x = 1.382
⇒ x = 3.6 or x = 1.4 (correct to two significant figures)
APPEARS IN
RELATED QUESTIONS
Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m2? If so, find its length and breadth.
Determine the nature of the roots of the following quadratic equation:
(b + c)x2 – (a + b + c)x + a = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
48x² – 13x -1 = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
