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16. The roots of the equation x+ 2px + q = Odiffer by 1. Show that p q - 4.

16. The roots of the equation x+ 2px + q = Odiffer by 1. Show that p q - 4.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 7DE
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Solve Q16, 17& 18 showing clearly all steps

(x-2)(x-1) 14. Given that y: ,X E R, x # -2, find the set of values of x for which v is real. Given that the rocts of the quadratic equation x+ (6- a)x + 2a = 0, arc real and equal, find the values of the real constant a. Using the smaller value of a. form a quadratic equation whose roots are - a + 2 and- ½ a, where a is the root of the equation: + (6- 9)x + 2a = 0 16. The roots of the equation x + 2px + q = 0differ by 1. Show that p = q + 1 V. Given that a + 1 and ß + 1 are the roois of the equation 2x-nx +n = constant, find, in terms of n the quadratic equation whose roots are a" and B- 2 Find the range of values of k for which the equation kx? (k-3)x + 1=0 has real and O where n is a distinct roots 5 Given that the equation (k- 3)x+ 4x + k 0 has real roots.find (a) the range of values of kab)the range of values of k for which the roots of the equation have the sanme Sign. 20. (ii) Given that p and q are the roots of the equation 9x- 4ax = -- (1 +6x), where a is a real constant, show that an equation whose roots are and is x² + (6- 4a)x + 9 3 0. 21. i) Given that the roots of the equation:x" - c = 0 are a and ß, form the quadratic 1. 1. equation whose roots are a + and 6 +
Transcribed Image Text:(x-2)(x-1) 14. Given that y: ,X E R, x # -2, find the set of values of x for which v is real. Given that the rocts of the quadratic equation x+ (6- a)x + 2a = 0, arc real and equal, find the values of the real constant a. Using the smaller value of a. form a quadratic equation whose roots are - a + 2 and- ½ a, where a is the root of the equation: + (6- 9)x + 2a = 0 16. The roots of the equation x + 2px + q = 0differ by 1. Show that p = q + 1 V. Given that a + 1 and ß + 1 are the roois of the equation 2x-nx +n = constant, find, in terms of n the quadratic equation whose roots are a" and B- 2 Find the range of values of k for which the equation kx? (k-3)x + 1=0 has real and O where n is a distinct roots 5 Given that the equation (k- 3)x+ 4x + k 0 has real roots.find (a) the range of values of kab)the range of values of k for which the roots of the equation have the sanme Sign. 20. (ii) Given that p and q are the roots of the equation 9x- 4ax = -- (1 +6x), where a is a real constant, show that an equation whose roots are and is x² + (6- 4a)x + 9 3 0. 21. i) Given that the roots of the equation:x" - c = 0 are a and ß, form the quadratic 1. 1. equation whose roots are a + and 6 +
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