In a quadratic equation of the form ax² + bx + c = 0, the sum of the solutions is given by the formula: x₁ + x₂ = -b/a
In this case, the sum of the solutions is:
3.5 + (-1) = -b/a
Simplifying:
2.5 = -b/a
On the other hand, the product of the solutions is given by the formula: x₁ * x₂ = c/a
In this case, the product of the solutions is:
3.5 * (-1) = -7/2
Simplifying:
-3.5 = -7/2
To find the value of k, we need to find the value of b. By comparing the coefficients of the quadratic equation, we can deduce that b = k - 3.
Substituting b = k - 3 into the equation -b/a = 2.5:
- (k - 3)/a = 2.5
Cross-multiplying:
-2.5a = k - 3
Simplifying:
k = -2.5a + 3
Now, using the equation -3.5 = -7/2:
-3.5 = -7/2
Multiplying both sides by 2:
-7 = -14/2
Simplifying:
-7 = -7
This equation is true for any value of a. Therefore, we can let a = 1. Substituting a = 1 into the equation k = -2.5a + 3:
k = -2.5(1) + 3
Simplifying:
k = -2.5 + 3
k = 0.5
Thus, the value of k is 0.5.
4. If the solution of 2x² + (k- 3) x - 7 = 0are 3.5 and -1,then what is the value of k?
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1 answer