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### High School Mathematics6.5 Forming a Quadratic Equation Using Its Roots

 Let a and b be the roots of the quadratic equation, then the required equation is x2 - (a + b)x + (a*b) = 0. Example: Find the quadratic equation whose roots are 5 and 3. Solution: Given that, roots of the equation are 5 and 3 Therefore, the required quadratic equation is x2 - (a + b)x + (a*b) = 0. Substituting the value of roots in the above equation we get the required equation. x2 - (5+3)x + 5*3 = 0 x2 - 8x + 15 = 0. Directions: Solve the following problems. Also write at least 5 examples of your own.
 Q 1: Find the quadratic equation whose roots are 3/4 and 1/2.8x2 - 10x + 38x2 - 10x - 38x2 - 8x + 38x2 + 10x + 3 Q 2: Find the quadratic equation whose roots are 9 and 1/2.2x2 + 19x + 92x2 - 14x + 92x2 - 19x + 92x2 - 19x - 9 Q 3: Find the quadratic equation whose roots are 1/2 and 3/2.4x2 - 6x + 34x2 - 8x - 34x2 - 8x + 34x2 + 8x + 3 Q 4: Find the quadratic equation whose roots are 6 and 3.x2 + 9x + 18x2 - 9x + 9x2 - 9x + 18x2 - 9x - 18 Q 5: Find the quadratic equation whose roots are 8 and -3.x2 - 5x - 24x2 - 11x - 24x2 - 8x - 24x2 + 5x - 24 Q 6: Find the quadratic equation whose roots are 9 and 3.x2 + 12x + 27x2 - 12x - 27x2 - 12x + 27x2 - 6x + 27 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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