Question

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Theratioofthesumandproductoftherootsoftheequatiद रेश्यो ऑफ द सम एंड प्रोडक्ट ऑफ द रूट्स ऑफ द इक्वेशन 3 एक्स स्क्वायर माइनस 12 प्लस 18 इज इक्वल टू जीरो ​

Answer 1

Answer:

Hope it will help you . Mark my answer as brainliest.

Explanation:

A "root" (or "zero") is where the polynomial is equal to zero:

Graph of Inequality

Put simply: a root is the x-value where the y-value equals zero.

General Polynomial

If we have a general polynomial like this:

f(x) = axn + bxn-1 + cxn-2 + ... + z

Then:

Adding the roots gives −b/a

Multiplying the roots gives:

z/a (for even degree polynomials like quadratics)

−z/a (for odd degree polynomials like cubics)

Which can sometimes help us solve things.

How does this magic work? Let's find out ...

Factors

We can take a polynomial, such as:

f(x) = axn + bxn-1 + cxn-2 + ... + z

And then factor it like this:

f(x) = a(x−p)(x−q)(x−r)...

Then p, q, r, etc are the roots (where the polynomial equals zero)

Quadratic

Let's try this with a Quadratic (where the variable's biggest exponent is 2):

ax2 + bx + c

When the roots are p and q, the same quadratic becomes:

a(x−p)(x−q)

Is there a relationship between a,b,c and p,q ?

Let's expand a(x−p)(x−q):

a(x−p)(x−q)

= a( x2 − px − qx + pq )

= ax2 − a(p+q)x + apq