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If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?
- a)-22.5
- b)16
- c)-10.5
- d)-17.5
- e)Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If one of the roots of the quadratic equation x2+ mx + 24 = 0 is 1.5, ...
The given quadratic equation is x2 + mx + 24 = 0
Substitute x = 1.5 in the above equation because 1.5 is a root of the equation.
(1.5)2 + 1.5m + 24 = 0
2.25 + 1.5m + 24 = 0
1.5m = -26.25 Or m
Substitute x = 1.5 in the above equation because 1.5 is a root of the equation.
(1.5)2 + 1.5m + 24 = 0
2.25 + 1.5m + 24 = 0
1.5m = -26.25 Or m
Most Upvoted Answer
If one of the roots of the quadratic equation x2+ mx + 24 = 0 is 1.5, ...
To find the value of 'm' in the quadratic equation, we can use the fact that the sum of the roots of a quadratic equation is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term.
Given that one of the roots is 1.5, we can use this information to find the value of 'm'.
Let's start by writing the quadratic equation in standard form:
x^2 + mx + 24 = 0
We know that one of the roots is 1.5, so we can write the equation as:
(x - 1.5)(x - r) = 0
Expanding this equation, we get:
x^2 - (1.5 + r)x + 1.5r = 0
Comparing this with the standard form equation, we can see that the coefficient of the linear term is -(1.5 + r) and the coefficient of the quadratic term is 1.
According to the sum of roots formula, the sum of the roots is equal to -(coefficient of the linear term) / (coefficient of the quadratic term).
So, we have:
1.5 + r = -(m/1)
Simplifying this equation, we get:
1.5 + r = -m
Now, we can solve for 'm' by substituting the given root value:
1.5 + 1.5 = -m
3 = -m
m = -3
Therefore, the value of 'm' is -3.
However, none of the given answer options match the calculated value of 'm'. Therefore, the correct answer is e) Cannot be determined, as the options provided do not include the correct value of 'm'.
Given that one of the roots is 1.5, we can use this information to find the value of 'm'.
Let's start by writing the quadratic equation in standard form:
x^2 + mx + 24 = 0
We know that one of the roots is 1.5, so we can write the equation as:
(x - 1.5)(x - r) = 0
Expanding this equation, we get:
x^2 - (1.5 + r)x + 1.5r = 0
Comparing this with the standard form equation, we can see that the coefficient of the linear term is -(1.5 + r) and the coefficient of the quadratic term is 1.
According to the sum of roots formula, the sum of the roots is equal to -(coefficient of the linear term) / (coefficient of the quadratic term).
So, we have:
1.5 + r = -(m/1)
Simplifying this equation, we get:
1.5 + r = -m
Now, we can solve for 'm' by substituting the given root value:
1.5 + 1.5 = -m
3 = -m
m = -3
Therefore, the value of 'm' is -3.
However, none of the given answer options match the calculated value of 'm'. Therefore, the correct answer is e) Cannot be determined, as the options provided do not include the correct value of 'm'.
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If one of the roots of the quadratic equation x2+ mx + 24 = 0 is 1.5, then what is the value of m?a)-22.5b)16c)-10.5d)-17.5e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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