Question
Download Solution PDFIf a and b are the zeroes of the quadratic polynomial p(x) = ax2 + bx + c, then which of the following is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Quadratic polynomial: p(x) = ax2 + bx + c
Zeroes: a and b
Formula used:
1) The sum of zeroes of a quadratic equation is given by a + b = -b/a.
2) The product of zeroes is given by ab = c/a.
3) The zeroes of the polynomial are the x-coordinates where the graph intersects the x-axis.
Calculation:
1) Sum of zeroes: The sum of the zeroes a and b of the quadratic polynomial p(x) = ax2 + bx + c is given by a + b = -b/a, which follows from Vieta's formulas.
2) Product of zeroes: The product of the zeroes a and b is given by ab = c/a, which also follows from Vieta's formulas.
3) Zeroes as x-coordinates: The points where the graph of the quadratic equation y = p(x) intersects the x-axis correspond to the values of x for which p(x) = 0. These are precisely the zeroes a and b.
∴ The correct answer is option 4: All of these.
Last updated on May 10, 2025
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