For the quadratic equation 0.4x2+bx−4.8=0, where b is a constant, the sum of the two solutions is equal to the product of the two solutions. What is the value of b?
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Cevap: 4.8
Cevap
The value of the constant b is 4.8.
According to Vieta's formulas, the sum of the solutions to the quadratic equation ax2+bx+c=0 is given by −ab and their product is given by ac. For the given equation 0.4x2+bx−4.8=0, the product of the solutions is 0.4−4.8=−12. Setting the sum equal to the product yields the equation −0.4b=−12. Multiplying both sides by −0.4 isolates b, giving b=4.8.
Adım Adım Çözüm
1
Identify the coefficients of the quadratic equation.
a=0.4, b=b, and c=−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 −0.4b and product of solutions is 0.4−4.8=−12.
To establish the mathematical relationship given in the problem.
3
Equate the sum and product of the solutions and solve for the constant b.
−0.4b=−12⟹b=−12×(−0.4)=4.8.
The problem states that the sum of the two solutions is equal to their product.