Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for zz.\newlinez2−10z+21=0z^2 - 10z + 21 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinez=__z = \_\_

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve polynomial equationsright chevron icon

Full solution

Q. Solve for zz.\newlinez2−10z+21=0z^2 - 10z + 21 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinez=__z = \_\_
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation z2−10z+21=0z^2 - 10z + 21 = 0, which is in the form az2+bz+c=0az^2 + bz + c = 0. Here, a=1a = 1, b=−10b = -10, and bb00.
  2. Factor the quadratic equation: Factor the quadratic equation. We need to find two numbers that multiply to give acac (which is 2121) and add up to give bb (which is −10-10).\newlineThe numbers that satisfy these conditions are −7-7 and −3-3 because (−7)×(−3)=21(-7) \times (-3) = 21 and (−7)+(−3)=−10(-7) + (-3) = -10.
  3. Write factored form: Write the factored form of the quadratic equation using the numbers found in Step 22.\newlinez2−10z+21=(z−7)(z−3)z^2 - 10z + 21 = (z - 7)(z - 3)
  4. Solve for z: Set each factor equal to zero and solve for z.\newlineFirst factor: (z−7)=0(z - 7) = 0\newlinez=7z = 7\newlineSecond factor: (z−3)=0(z - 3) = 0\newlinez=3z = 3

More problems from Solve polynomial equations

Question
Find the degree of this polynomial.\newline`5b^{10} + 3b^3`\newline_______
Get tutor helpright-arrow

Posted 5 months ago

Question
Subtract.\newline(9a+5)−(2a+4)(9a + 5) - (2a + 4)\newline____
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the product. Simplify your answer. \newline−3v2(v2−9)-3v^2(v^2 - 9)\newline________
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the product. Simplify your answer.\newline(v−3)(4v+1)(v - 3)(4v + 1)\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the square. Simplify your answer.\newline(3y+2)2(3y + 2)^2\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Divide. If there is a remainder, include it as a simplified fraction.\newline(24t2+36t)÷6t(24t^2 + 36t) \div 6t\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Is the function q(x)=x6−9 q(x) = x^6 - 9 even, odd, or neither?\newlineChoices:\newline[[even][odd][neither]]\text{[[even][odd][neither]]}
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the product. Simplify your answer. \newline−3q2(−3q2+q)-3q^2(-3q^2 + q)\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the product. Simplify your answer.\newline(r+3)(4r+2)(r + 3)(4r + 2)\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the roots of the factored polynomial.\newline(x+7)(x+4)(x + 7)(x + 4)\newlineWrite your answer as a list of values separated by commas.\newlinex=x = ____
Get tutor helpright-arrow

Posted 9 months ago

View all (29)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant