Question

Form a quadratic polynomial whose one of the zero is -15 and the sum of the zeros is 42

Answer 1

Step-by-step explanation:

form of quadratic equation->

x^2 - (sum of roots)x + (product of roots)

Answer 2

Step-by-step explanation:

◼As we have given ,

sum of the roots of the quadratic polynomial is 42 and one of its root is (-15)

◾let us consider the roots of the quadratic polynomial are α and β

Therefor, as a given conditions

α + β = 42 ................(1)

◾ And here one of the root is α = (-15)

◾put the value of α in equation(1)

➡(-15) + β = 42

➡β = 42 + 15 = 57

β = 57

◾therefor the second root of the quadratic polynomial is β = 57

◾we know the formula to making a quadratic equation if the roots of the equations are α and β , formula is

${x}^{2} - ( \alpha + \beta )x + \alpha \times \beta$

◾so, first we have to find values of ( α + β ) and (α x β )

➡α + β = ( -15 ) + 57

= 42

➡α x β = ( -15 ) x ( 57)

= -855

◾Now, put the values of (α + β ) and (α x β ) in a equation

${x}^{2} - ( 42 )x + ( - 855 )$

${x}^{2} - 42x - 855 = 0$

◾So the equation whose one of the zero is -15 and the sum of the zeros is 42 is

x² - 42 x - 855 =0