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1. 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

   What is a quadratic equation?

   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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