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Quadratic Equations and the Quadratic Formula

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For the quadratic equation 0.4x2+bx−4.8=00.4x^2 + bx - 4.8 = 0, where bb is a constant, the sum of the two solutions is equal to the product of the two solutions. What is the value of bb?

Show answer & explanation

Answer: 4.8

Answer

The value of the constant bb is 4.84.8.
According to Vieta's formulas, the sum of the solutions to the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 is given by −ba-\frac{b}{a} and their product is given by ca\frac{c}{a}. For the given equation 0.4x2+bx−4.8=00.4x^2 + bx - 4.8 = 0, the product of the solutions is −4.80.4=−12\frac{-4.8}{0.4} = -12. Setting the sum equal to the product yields the equation −b0.4=−12-\frac{b}{0.4} = -12. Multiplying both sides by −0.4-0.4 isolates bb, giving b=4.8b = 4.8.

Step-by-Step Solution

1
Identify the coefficients of the quadratic equation.
a=0.4a = 0.4, b=bb = b, and c=−4.8c = -4.8.
To apply formulas relating the coefficients to the solutions.
2
Express the sum and product of the solutions using Vieta's formulas.
Sum of solutions is −b0.4-\frac{b}{0.4} and product of solutions is −4.80.4=−12\frac{-4.8}{0.4} = -12.
To establish the mathematical relationship given in the problem.
3
Equate the sum and product of the solutions and solve for the constant bb.
−b0.4=−12  ⟹  b=−12×(−0.4)=4.8-\frac{b}{0.4} = -12 \implies b = -12 \times (-0.4) = 4.8.
The problem states that the sum of the two solutions is equal to their product.

Key Concept

Sum and Product of Roots (Vieta's Formulas)
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