Advertisements
Advertisements
प्रश्न
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the value of the discriminant in the following quadratic equation :
x2 +2x+4=0
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only
x2 - 4x - 1 = 0
Solve x2/3 + x1/3 - 2 = 0.
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax2 + bx + c = 0 is:
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
Which of the following equations has the sum of its roots as 3?
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
