Give the values a, b, and c needed to write the equations standard form. 2/3(x - 4)(x + 5)=1
Solution:
Given equation is 2/3(x - 4)(x + 5)=1
The standard form of the quadratic equation is ax2+bx+c=0 Where a, b are the coefficients of x, and c is the constant term. The first condition for an equation to be a quadratic equation is that the coefficient of x2 is a non-zero term(a ≠0). For writing a quadratic equation, the numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.
Cross multiplying the terms of the given equation 2/3 (x - 4) (x + 5)=1
2(1) = 3(x - 4)(x + 5)
2 = 3[x2- 4x + 5x + 20]
2 = 3[x2 + x +20]
2 = 3x2 + 3x + 60
2 = 3x2 + 3x + 60
3x2 + 3x + 60 - 2 = 0
3x2 + 3x + 58 = 0.
The equivalent quadratic form of the given equation is 3x2 + 3x + 58 = 0.
Comparing the equation 3x2+ 3x + 58 = 0 with the standard form of quadratic equation ax2+bx+c=0
a =3 ,b= 3 and c =58
Give the values a, b, and c needed to write the equations in standard form. 2/3(x-4)(x+5)=1
Summary:
The values of a,b and c so that the equation23(x-4)(x+5)=1 in the standard quadratic equation are a =3 ,b= 3 and c =58
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