Study the relationship between zeroes and coefficients of quadratic polynomials, and find polynomials from given zeroes.
For ax²+bx+c with zeroes α and β: sum of zeroes=-b/a, product of zeroes=c/a.
Find the sum and product of zeroes of x²-5x+6.
sum=5, product=6 (matches roots 2,3)
Find the sum and product of zeroes of 2x²+3x-5.
sum=-3/2, product=-5/2
Find the sum and product of zeroes of 2x²-7x+3.
sum=7/2, product=3/2
A quadratic polynomial can be built from its zeroes using: x²-(sum of zeroes)x+(product of zeroes).
Find a quadratic polynomial with zeroes 3 and -2.
sum=1, product=-6; polynomial: x²-x-6
Find a quadratic polynomial with zeroes 1/2 and 1/3.
sum=5/6, product=1/6; polynomial: x²-5x/6+1/6, or 6x²-5x+1
Find a quadratic polynomial with zeroes -3 and 5.
sum=2, product=-15; polynomial: x²-2x-15
1. Find the sum and product of zeroes of x²-7x+12.
2. Find the sum and product of zeroes of 3x²-2x-1.
3. Find a quadratic polynomial with zeroes 4 and -1.
4. Find a quadratic polynomial with zeroes 2/3 and -1.
5. If one zero of x²-8x+k is 3, find k.
6. Find the sum and product of zeroes of x²-9x+14.
7. Find the sum and product of zeroes of 4x²+5x-6.
8. Find a quadratic polynomial with zeroes 6 and -2.
9. Find a quadratic polynomial with zeroes 1/2 and -3.
10. If one zero of x²-11x+k is 7, find k.