Anita checks whether x = 3 is a zero of p(x) = 2x² − 5x − 3 by evaluating p(3). What does she find?

Anita checks whether $x = 3$ is a zero of $p (x) = 2 x^{2} - 5 x - 3$ by evaluating $p$ (3). What does she find?

Class 10PolynomialsAlgebra — Polynomials

A $p (3) = 6$ , so 3 is not a zero of $p (x)$
B $p (3) = 0$ , so 3 is a zero of $p (x)$
C $p (3) = 0$ , so 3 is not a zero of $p (x)$
D $p (3) = 30$ , so 3 is a zero of $p (x)$

Step-by-Step Solution

p (3) = 2 (9) - 5 (3) - 3 = 18 - 15 - 3 = 0

. A value of 0 is exactly what makes 3 a zero, so 3 is a zero and

(x - 3)

is a factor. The value 30 comes from adding 5(3) instead of subtracting it, 6 from adding the last 3, and the third option reverses what the test means.

Answer: B)

p (3) = 0

, so 3 is a zero of

p (x)

Key idea: Geometric meaning of zeros

Zeros of

p (x)

are exactly the **

x

-coordinates where the graph

y = p (x)

meets the

x

-axis**.

- **Linear**

y

= ax +

b

: graph is a straight line, crosses

x

-axis ONCE → exactly 1 zero.
- **Quadratic**

y = a x^{2} + b x + c

: graph is a parabola. Possible cases:
- Crosses

x

-axis at 2 points → 2 distinct real zeros.
- Touches

x

-axis at 1 point → 1 repeated zero (vertex on

x

-axis).
- Does not meet

x

-axis → no real zeros.
- **Cubic**

y = a x^{3}

+ …: shape is a curve that crosses 1, 2, or 3 times → 1, 2, or 3 real zeros.

So 'find the zeros' is the algebraic version of 'find where the graph crosses the

x

-axis'.

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Anita checks whether x=3 is a zero of p(x)=2x2−5x−3 by evaluating p(3). What does she find?

Step-by-Step Solution

Key idea: Geometric meaning of zeros

Master this chapter in 30 minutes a day.

More Class 10 Polynomials practice

Anita checks whether $x = 3$ is a zero of $p (x) = 2 x^{2} - 5 x - 3$ by evaluating $p$ (3). What does she find?