The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645
In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:
x²
When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -
x² = 3 -
When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x
x² = 3 - 4x
Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0
Where:
- a= 1
- b= 4
- c= -3
Solving the quadratic question we get the values for the (x) number
x= {- b ± √ [b² - (4* a*c)]} / (2 *a)
x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)
x= {- 4 ± √ (16 + 12)} / 2
x= {- 4± √ 28} / 2
x= (- 4 ± 5.29 ) / 2
x1= (- 4 + 5.29 ) / 2
x1= (1,29) / 2
x1= 0.645
x2= (- 4 - 5.29 ) / 2
x2= (9.29) / 2
x2= -4.645
We can check the values, replacing them into the equation:
(x1)² = 3 - 4(x1)
(0.645)² = 3 - 4*(0.645)
0.42 = 0.42
(x2)² = 3 - 4(x2)
(-4.645)² = 3 - 4*(-4.645)
21.58 = 21.58
<h3>What is a quadratic equation?</h3>It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:
ax²+ bx + c = 0
Learn more about quadratic equation at: brainly.com/question/25841119 and brainly.com/question/7784687
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