Most popular questions and responses by Jayden Haddy
1. maths

If one of the root of the quadratic equation ax^2 + bx +c =0 is three times the other, show that 3b^2 = 16ac

2. maths

prove that if m is not equal to n, the equation (m^2+n^2)x^2 - 2(m+n)x + 2=0 has unreal roots.

3. maths

Consider the quadratic equation m^2 x^2 + 2(2m-5)x + 8 = 0 a) If 2 is a root of the equation, find the possible values of m (there are four possible values) b) For each value of m, find the other root I have actually calculated the answer m=1 or m=-3 for

4. maths

If the ratio of the roots of the quadratic equation ax^2 + bx +c =0 is m:n prove that mnb^2=(m+n)^2 ac

5. maths

Consider the equation x(square) + 4px + 2q = 0 where p and q are real constants. a) by completing square, show that (x+2p)square =4P(SQUARE)-2q b) Hence show that x= -2p +/- square root(4 p(square) -2p ) c) Use the above results to solve the equations 1)

6. maths

Let ( x(square)+ 3x +1) over (2 x(square) -5x+2) = k ----------be y 1) Express y in the form of a x(square) + bx +c =0 2) If -3/4 is a root of y, find the value of k I don't really understand why the answer is like that. Can you explain?

7. maths

If the sum of the squares of the roots of the quadratic equation ax^2 + bx + c = 0 is m:n, prove that b^2= 2ac + 4a^2 I really have no idea how to prove it so pls help

8. maths

Find the value of k if the product of the roots of the quadratic equation kx^2 + 4x + k^2 -21 = 0 is 4

if a, b,c are real numbers and not all equal, prove that the equation (c-a)x^2 -2(a-b)x + (b+c) = 0 has unequal real roots

10. maths

x^2 - 20x +c =0 one of the root of the equation is the three times the other, find the values of c and the roots

11. maths

if a, b,c are real numbers and not all equal, prove that the equation (c-a)x^2 -2(a-b)x + (b+c) = 0 has unequal real roots

12. maths

given that a,b,c are real numbers and c is bigger than 0, prove that the roots of the equation (x-a)(x-b)=c are real.

13. maths

Prove that if p and q are rational and p is not equal to 0, the roots of the quadratic equations p x(square) + 2qx -p +2q = 0.

14. maths

solve the following equation by completing the square x(square) - 4(square root 5)x =6 = 0 Then x= or x=

15. maths

solve the following equation by completing square x(square) + 5x - 84 Pls show steps x= or x=

16. maths

Consider the quadratic equation m^2 x^2 + 2(2m-5)x + 8 = 0 a) If 2 is a root of the equation, find the possible values of m (there are four possible values) b) For each value of m, find the other root

17. maths

If the roots of x^2 - px + q = 0 are two consecutive integers, prove that p^2 - 4q -1 = 0

18. maths

a)If one root of the equation x^2 + a(3a-5)x = 2(x+4a) is negative of the other. Find the values of a . b) If a>0, use the result of (a) to solve the equation.

19. maths

Given that a and b are the roots of the quadratic equation 2x^2 - 4x +3 = 0, find the quadratic equation in x with roots a^2-(1/b) and b^2-(1/a).

20. maths

If the roots of the quadratic equation 4x^2 + px +5 = 0 are a and a+2, find the real values of p .

21. maths

Prove that if p and q are rational and p is not equal to 0, the roots of the quadratic equations p x(square) + 2qx -p +2q = 0 are rational.

22. maths

Find the discriminant of the equations in terms of k k x(square)-(3k-5)x +14 = 0

23. maths

Let ( x(square)+ 3x +1) over (2 x(square) -5x+2) = k ----------be y 1) Express y in the form of a x(square) + bx +c =0 2) If -3/4 is a root of y, find the value of k