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What is the value of s+t if the equation 3x2 + tx + s has 2 and 3 as its roots?
- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the value of s+t if the equation 3x2 + tx + s has 2 and 3 as i...
- Given the equation 3x² + tx + s = 0 with roots 2 and 3:
- Sum of roots: 2 + 3 = 5 ⇒ -t /3 = 5 ⇒ t = -15
- Product of roots: 2 × 3 = 6 ⇒ s /3 = 6 ⇒ s = 18
- s + t = 18 + (-15) = 3
- Answer: 3
Most Upvoted Answer
What is the value of s+t if the equation 3x2 + tx + s has 2 and 3 as i...
Understanding the Problem
To find the values of s and t in the quadratic equation 3x² + tx + s, given that its roots are 2 and 3, we can use Vieta's formulas.
Vieta's Formulas
According to Vieta's formulas for a quadratic equation ax² + bx + c = 0, the relationships between the coefficients and the roots (r1 and r2) are:
- Sum of the roots (r1 + r2) = -b/a
- Product of the roots (r1 * r2) = c/a
In our case:
- Roots are 2 and 3
- a = 3, b = t, c = s
Calculating the Sum of the Roots
Using the sum of the roots:
- r1 + r2 = 2 + 3 = 5
- Therefore, -t/3 = 5
This gives us:
- t = -15
Calculating the Product of the Roots
Using the product of the roots:
- r1 * r2 = 2 * 3 = 6
- Therefore, s/3 = 6
This gives us:
- s = 18
Finding s + t
Now we can calculate s + t:
- s + t = 18 + (-15) = 3
Conclusion
Thus, the value of s + t is 3. The correct answer is option 'C'.
To find the values of s and t in the quadratic equation 3x² + tx + s, given that its roots are 2 and 3, we can use Vieta's formulas.
Vieta's Formulas
According to Vieta's formulas for a quadratic equation ax² + bx + c = 0, the relationships between the coefficients and the roots (r1 and r2) are:
- Sum of the roots (r1 + r2) = -b/a
- Product of the roots (r1 * r2) = c/a
In our case:
- Roots are 2 and 3
- a = 3, b = t, c = s
Calculating the Sum of the Roots
Using the sum of the roots:
- r1 + r2 = 2 + 3 = 5
- Therefore, -t/3 = 5
This gives us:
- t = -15
Calculating the Product of the Roots
Using the product of the roots:
- r1 * r2 = 2 * 3 = 6
- Therefore, s/3 = 6
This gives us:
- s = 18
Finding s + t
Now we can calculate s + t:
- s + t = 18 + (-15) = 3
Conclusion
Thus, the value of s + t is 3. The correct answer is option 'C'.
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Question Description
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