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In a quadratic equation with leading coefficient 1, a student reads the coefficient 16 of x wrongly as 19 and obtain the roots as -15 and -4. The correct roots are
- a)6, 10
- b)-6, -10
- c)-7, -9
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a quadratic equation with leading coefficient 1, a student reads th...
Since coefficient of x = 16,
∴ sum of roots = -16
Since constant term = (-15)(-4) = 60,
∴ correct answer is -6, -10
∴ sum of roots = -16
Since constant term = (-15)(-4) = 60,
∴ correct answer is -6, -10
Most Upvoted Answer
In a quadratic equation with leading coefficient 1, a student reads th...
Given information:
- The leading coefficient of the quadratic equation is 1.
- The student read the coefficient 16 of x wrongly as 19.
- The student obtained the roots as -15 and -4.
Let's solve the quadratic equation:
The quadratic equation can be written as:
x^2 + (sum of roots)x + (product of roots) = 0
The sum of roots is given by the formula:
Sum of roots = -b/a
The product of roots is given by the formula:
Product of roots = c/a
Using the given information:
- The sum of roots is -15 + (-4) = -19.
- The product of roots is -15 * (-4) = 60.
Calculating the correct coefficient of x:
Using the formula for the sum of roots, we have:
-19 = -b/1
b = 19
Therefore, the correct coefficient of x is 19.
Calculating the correct roots:
Using the formula for the product of roots, we have:
60 = c/1
c = 60
The quadratic equation with the correct coefficients is:
x^2 + 19x + 60 = 0
Factoring the quadratic equation:
To find the correct roots, we need to factor the quadratic equation.
The factors of 60 that add up to 19 are 4 and 15.
Therefore, the factored form of the quadratic equation is:
(x + 4)(x + 15) = 0
Setting each factor equal to zero, we have:
x + 4 = 0 or x + 15 = 0
Solving for x, we get:
x = -4 or x = -15
Therefore, the correct roots of the quadratic equation are -4 and -15.
Conclusion:
The correct roots of the quadratic equation with the correct coefficient of x are -4 and -15. Therefore, the correct answer is option B: -6, -10.
- The leading coefficient of the quadratic equation is 1.
- The student read the coefficient 16 of x wrongly as 19.
- The student obtained the roots as -15 and -4.
Let's solve the quadratic equation:
The quadratic equation can be written as:
x^2 + (sum of roots)x + (product of roots) = 0
The sum of roots is given by the formula:
Sum of roots = -b/a
The product of roots is given by the formula:
Product of roots = c/a
Using the given information:
- The sum of roots is -15 + (-4) = -19.
- The product of roots is -15 * (-4) = 60.
Calculating the correct coefficient of x:
Using the formula for the sum of roots, we have:
-19 = -b/1
b = 19
Therefore, the correct coefficient of x is 19.
Calculating the correct roots:
Using the formula for the product of roots, we have:
60 = c/1
c = 60
The quadratic equation with the correct coefficients is:
x^2 + 19x + 60 = 0
Factoring the quadratic equation:
To find the correct roots, we need to factor the quadratic equation.
The factors of 60 that add up to 19 are 4 and 15.
Therefore, the factored form of the quadratic equation is:
(x + 4)(x + 15) = 0
Setting each factor equal to zero, we have:
x + 4 = 0 or x + 15 = 0
Solving for x, we get:
x = -4 or x = -15
Therefore, the correct roots of the quadratic equation are -4 and -15.
Conclusion:
The correct roots of the quadratic equation with the correct coefficient of x are -4 and -15. Therefore, the correct answer is option B: -6, -10.
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Community Answer
In a quadratic equation with leading coefficient 1, a student reads th...
Let any quad eq be in the form ax2+bx+c=0
sum of zeroes =-b/a= -15-4=-19
it means b=19
product of zeroes=c/a= -15×-4=60
so x2+19x+60
x2+16x+60
the roots will be -10,-6
sum of zeroes =-b/a= -15-4=-19
it means b=19
product of zeroes=c/a= -15×-4=60
so x2+19x+60
x2+16x+60
the roots will be -10,-6
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In a quadratic equation with leading coefficient 1, a student reads the coefficient 16 of x wrongly as 19 and obtain the roots as -15 and -4. The correct roots area)6, 10b)-6, -10c)-7, -9d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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