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Home > Algebra calculators > Quadratic Equation
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1. Complete square, Is perfect square, Find missing term
1. Completing the square for quadratic equation
eg. `9x^2+6x+1= 9( x+1/3 )^2`
2. Determining if the polynomial is a perfect square
eg. (1) `x^2-4xy+4y^2`, (2) `3x^2+5x+2`
3. Find the missing term in a perfect square trinomial
eg. (1) `9x^2` - __ + 16, (2) __ + `12x^2` + 9, (3) `49x^2` + 56 xy + __
2. Quadratic Equation
1.1 Solving quadratic equations by factoring,
eg. (1) `25x^2-30x+9=0`, (2) `x^2+10x-56=0`
1.2 Solving quadratic equations using the quadratic formula,
eg. (1) `25x^2-30x+9=0`, (2) `x^2+10x-56=0`
1.3 Discriminant
eg. (1) `25x^2-30x+9=0`, (2) `x^2+10x-56=0`
1.4 Discriminant & Nature of Roots
eg. (1) `25x^2-30x+9=0`, (2) `x^2+10x-56=0`
2. Find the quadratic equation whose roots are `alpha` and `beta`
eg. (1) `alpha=3, beta=-4`, (2) `alpha=1+3sqrt(2), beta=1-3sqrt(2)`
3. Roots for non-zero denominator
eg. (1) `(5x-18)/(x+2)=(2x-6)/(x-1)`, (2) `(x)/(x+1)+(x+1)/(x)=5/2`,
(3) `4((4x+1)/(4x-1))^(2)+(4x+1)/(4x-1)=3`, (4) `(4x+1)/(4x-1)+(4x-1)/(4x+1)=3`
4. Roots of non-quadratic equation
eg. (1) `6(x^2+1/x^2)-25(x-1/x)+12=0`, (2) `(x^2+1/x^2)-8(x+1/x)+14=0`
5. If `alpha` and `beta` are roots of equation `2x^2-3x-6=0`, then find `alpha^2+beta^2`
6. If `alpha` and `beta` are roots of equation `2x^2-3x-6=0`, then find equation whose roots are `alpha^2` and `beta^2`
7. Find value of `k` for which `2x^2+kx+2=0` has real roots
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