find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively 1 upon 4 and -1 About the author Piper
Sum of zeroes = 1/4 = -b/a [tex] \alpha + \beta [/tex] Product of zeroes = -1 = c/a [tex] \alpha . \beta [/tex] [tex] \sf {x}^{2} – ( \alpha + \beta ) + \alpha . \beta \\ \\ \sf \: = {x}^{2} – \frac{1}{4} + ( -1) \\ \\ \sf \: multiply \: \: \: {eq}^{n} \: \: \: by \: \: \: 4 \\ \\ \boxed{ \green{{ = \sf \: 4 {x}^{2} – 1 – 4}}}[/tex] Reply
Sum of zeroes = 1/4 = -b/a
[tex] \alpha + \beta [/tex]
Product of zeroes = -1 = c/a
[tex] \alpha . \beta [/tex]
[tex] \sf {x}^{2} – ( \alpha + \beta ) + \alpha . \beta \\ \\ \sf \: = {x}^{2} – \frac{1}{4} + ( -1) \\ \\ \sf \: multiply \: \: \: {eq}^{n} \: \: \: by \: \: \: 4 \\ \\ \boxed{ \green{{ = \sf \: 4 {x}^{2} – 1 – 4}}}[/tex]