Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To find a quadratic polynomial whose zeroes are -4 and -5, we can use the relationship between the roots of a polynomial and its coefficients.
Let's denote the zeroes of the quadratic polynomial as [tex]\(\alpha = -4\)[/tex] and [tex]\(\beta = -5\)[/tex].
For a quadratic polynomial of the form [tex]\(ax^2 + bx + c\)[/tex]:
1. Sum of the roots ([tex]\(\alpha + \beta\)[/tex]):
[tex]\[ \alpha + \beta = -4 + (-5) = -9 \][/tex]
2. Product of the roots ([tex]\(\alpha \times \beta\)[/tex]):
[tex]\[ \alpha \beta = -4 \times -5 = 20 \][/tex]
Using these results, we can construct the quadratic polynomial in the form:
[tex]\[ ax^2 + bx + c \][/tex]
Substituting [tex]\(a = 1\)[/tex] (since we often use the simplest form where the coefficient of [tex]\(x^2\)[/tex] is 1), we get:
[tex]\[ x^2 - (sum \ of \ roots)x + (product \ of \ roots) \][/tex]
Thus, plugging in the sum and product of the roots:
[tex]\[ x^2 - (-9)x + 20 \][/tex]
Simplifying this, we obtain:
[tex]\[ x^2 + 9x + 20 \][/tex]
Therefore, the quadratic polynomial whose zeroes are -4 and -5 is:
[tex]\[ x^2 + 9x + 20 \][/tex]
Let's denote the zeroes of the quadratic polynomial as [tex]\(\alpha = -4\)[/tex] and [tex]\(\beta = -5\)[/tex].
For a quadratic polynomial of the form [tex]\(ax^2 + bx + c\)[/tex]:
1. Sum of the roots ([tex]\(\alpha + \beta\)[/tex]):
[tex]\[ \alpha + \beta = -4 + (-5) = -9 \][/tex]
2. Product of the roots ([tex]\(\alpha \times \beta\)[/tex]):
[tex]\[ \alpha \beta = -4 \times -5 = 20 \][/tex]
Using these results, we can construct the quadratic polynomial in the form:
[tex]\[ ax^2 + bx + c \][/tex]
Substituting [tex]\(a = 1\)[/tex] (since we often use the simplest form where the coefficient of [tex]\(x^2\)[/tex] is 1), we get:
[tex]\[ x^2 - (sum \ of \ roots)x + (product \ of \ roots) \][/tex]
Thus, plugging in the sum and product of the roots:
[tex]\[ x^2 - (-9)x + 20 \][/tex]
Simplifying this, we obtain:
[tex]\[ x^2 + 9x + 20 \][/tex]
Therefore, the quadratic polynomial whose zeroes are -4 and -5 is:
[tex]\[ x^2 + 9x + 20 \][/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.